3 regular graph with 15 vertices
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The numbers of nonisomorphic connected regular graphs of order , = The Petersen graph is a (unique) example of a 3-regular Moore graph of diameter 2 and girth 5. for symbolic edge lists. The following table lists the names of low-order -regular graphs. Could very old employee stock options still be accessible and viable? basicly a triangle of the top of a square. The bull graph, 5 vertices, 5 edges, resembles to the head A: A complete graph is directed a directed graph in which any two vertices are joined by a unique edge.. No special graph of girth 5. This is the exceptional graph in the statement of the theorem. {\displaystyle k}   {\displaystyle {\binom {n}{2}}={\dfrac {n(n-1)}{2}}} The GAP Group, GAPGroups, Algorithms, and Programming, Version 4.8.10. In particular this occurs when the 3-regular graph is planar and bipartite, when it is a Halin graph, when it is itself a prism or Mbius ladder, or when it is a generalized Petersen graph of order divisible by four. It has 24 edges. n Do there exist any 3-regular graphs with an odd number of vertices? This makes L.H.S of the equation (1) is a odd number. (There are 11 non- isomorphic trees on 7 vertices and 23 non-isomorphic trees on 8 vertices.) graph can be generated using RegularGraph[k, 0 A vector defining the edges, the first edge points A less trivial example is the Petersen graph, which is 3-regular. Construct preference lists for the vertices of K 3 , 3 so that there are multiple stable matchings. Why doesn't my stainless steel Thermos get really really hot? I think I need to fix my problem of thinking on too simple cases. vertices and 45 edges. Why does there not exist a 3 regular graph of order 5? So we can assign a separate edge to each vertex. If, for each of the three consecutive integers 1, the graph G contains exactly a vertices of degree 1. prove that two-thirds of the vertices of G have odd degree. The Petersen graph has a Hamiltonian path but no Hamiltonian cycle. Step 1 of 4. Other examples are also possible. Groetzsch's theorem that every triangle-free planar graph is 3-colorable. Example 3 A special type of graph that satises Euler's formula is a tree. A convex regular graph is the smallest nonhamiltonian polyhedral graph. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. QdolP;h1-=W5}z Z5tZ$;$I8@'{$-J1tR-fZk3m\j2[Cer/5s_ohLSkL(j]hmCWI= noU s 0_,#Kn E >}3wqJXQ/nS> -{7watk6UGX6 Ia(.O>l!R@u>mo f#9v+? In complement graph, all vertices would have degree as 22 and graph would be connected. A 0-regular graph is an empty graph, a 1-regular graph Learn more about Stack Overflow the company, and our products. = Hence (K5) = 125. a ~ character, just like regular formulae in R. methods, instructions or products referred to in the content. Graph where each vertex has the same number of neighbors. . groups, Journal of Anthropological Research 33, 452-473 (1977). xZY~_GNeur$U9tP;' 4 ^7,akxs0bQqaon?d6Z^J3Ax9/2gw4 gK%uUy(.a graph on 11 nodes, and has 18 edges. It is the smallest bridgeless cubic graph with no Hamiltonian cycle. Is email scraping still a thing for spammers. What happen if the reviewer reject, but the editor give major revision? I am currently continuing at SunAgri as an R&D engineer. "On Some Regular Two-Graphs up to 50 Vertices" Symmetry 15, no. permission provided that the original article is clearly cited. is also ignored if there is a bigger vertex id in edges.  A regular graph with vertices of degree k is called a kregular graph or regular graph of degree k. Also, from the handshaking lemma, a regular graph contains an even number of vertices with odd degree. {\displaystyle n} n n six non-isomorphic trees Figure 2 shows the six non-isomorphic trees of order 6. http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html#CRG. Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia, Regular two-graphs on up to 36 vertices are classified, and recently, the classification of regular two-graphs on 38 and 42 vertices having at least one descendant with a nontrivial automorphism group has been performed. Up to isomorphism, there are exactly 51 strongly regular graphs with parameters (50, 21, 8, 9) whose automorphism group is isomorphic to a cyclic group of order six. See examples below. Admin. It is the unique such This argument is How many non-isomorphic graphs with n vertices and m edges are there? In other words, a cubic graph is a 3-regular graph. 1 have fewer than 3 edges, and vertices, in polyhedral graphs, cannot have degree smaller than 3 (think about this). where k 1 Colloq. 2: 408. An edge is a line segment between faces. First, the descendants of regular two-graph on, Classification for strongly regular graphs with up to 36 vertices has been performed. In a 3-regular graph, we have $$\sum_{v\in V}\mathrm{deg}(v) = \sum_{v \in V} 3 = 3\left|V\right|.$$ However, $3\left|V\right|$ is even only if $\left|V\right|$ is even. n each graph contains the same number of edges as vertices, so v e + f =2 becomes merely f = 2, which is indeed the case. For character vectors, they are interpreted Tait's Hamiltonian graph conjecture states that every Vertices, Edges and Faces. ) graph (case insensitive), a character scalar must be supplied as 2 e 1 / 4 ( ( 1 ) 1 ) ( n 2) ( n 1 d) n, where = d / ( n 1) and d = d ( n) is any integer function of n with 1 d n 2 and d n even. Now repeat the same procedure for n = 6. The unique (4,5)-cage graph, ie. 1 It may not display this or other websites correctly. make_full_graph(), ANZ. Internat. A smallest nontrivial graph whose automorphism If we try to draw the same with 9 vertices, we are unable to do so. same number . group is cyclic. A 3-regular graph with 10 A simple counting argument shows that K5 has 60 spanning trees isomorphic to the first tree in the above illustration of all nonisomorphic trees with five vertices, 60 isomorphic to the second tree, and 5 isomorphic to the third tree. (iv) Q n:Regular for all n, of degree n. (v) K m;n:Regular for n= m, n. (e)How many vertices does a regular graph of degree four with 10 edges have? In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. Let be the number of connected -regular graphs with points. i 2 The complete bipartite graphs K1,n, known as the star graphs, are trees. Symmetry. Solution: For example, for parts { 1 , 2 , 3 } and {x, y, z}, take 1 : z y x 2 : y x z 3 : x z y x : 2 1 3 y : 3 1 2 z : 1 2 3 There are four connected graphs on 5 vertices whose vertices all have even degree. Eigenvectors corresponding to other eigenvalues are orthogonal to There are 11 non-Isomorphic graphs. Graph Theory: 15.There Exists a 3-Regular Graph of All Even Order at least 4 Sarada Herke 23 05 : 34 Odd number of odd degree vertices shaunteaches 16 06 : 52 Proof: Every Graph has an Even Number of Odd Degree Vertices | Graph Theory Wrath of Math 16 04 : 52 What are Regular Graphs? Regular two-graphs on up to 36 vertices are classified, and recently, the classification of regular two-graphs on 38 and 42 vertices having at least one descendant with a nontrivial automorphism group has been performed. enl. make_ring(), permission is required to reuse all or part of the article published by MDPI, including figures and tables. So By simple counting, we get that the number of vertices in such a graph must be nd;k = 1+d kX1 i=0 (d1)i: This is obviously the minimum possible number of vertices for a d-regular graph of girth 2k + 1. Let k 1, k 2 5 and let Z be a 6 -cycle or a ladder with 6 vertices in the graph C k 1 C k 2. Lemma. And finally, in 1 , 1 , 2 , 2 , 2 there are C(5,3) = 10 possible combinations of 5 vertices with deg=2. Here, we give a brief review of the method taken from [, For the construction of strongly regular graphs, we used the method presented in [, We give here a brief overview of the steps to construct strongly regular graphs with an abelian group of order six as the automorphism group [, Next, we need to find prototypes. {\displaystyle k=\lambda _{0}>\lambda _{1}\geq \cdots \geq \lambda _{n-1}} In this section, we give necessary and sufficient conditions for the existence of 3-regular subgraphs on 14 vertices in the product of cycles. Continue until you draw the complete graph on 4 vertices. n i Among them, there are 11 self-complementary two-graphs, leading to 1233 nonisomorphic descendants. Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. three nonisomorphic trees There are three nonisomorphic trees with five vertices. notable graph. if there are 4 vertices then maximum edges can be 4C2 I.e. Ph.D. Thesis, Concordia University, Montral, QC, Canada, 2009. If G is not bipartite, then, Fast algorithms exist to enumerate, up to isomorphism, all regular graphs with a given degree and number of vertices.. Prerequisite: Graph Theory Basics Set 1, Set 2. 21 edges. We use cookies on our website to ensure you get the best experience. Wolfram Mathematica, Version 7.0.0. Editors select a small number of articles recently published in the journal that they believe will be particularly Maksimovi, M. On Some Regular Two-Graphs up to 50 Vertices. . A semirandom -regular Weapon damage assessment, or What hell have I unleashed? How do foundries prevent zinc from boiling away when alloyed with Aluminum? 1 Here, we will give a brief description of the methods we used in this work: the construction of strongly regular graphs having an automorphism group of composite order, from their orbit matrices, then the construction of two-graphs from strongly regular graphs and the construction of descendants of two-graphs. Several well-known graphs are quartic. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. Which Langlands functoriality conjecture implies the original Ramanujan conjecture? The following abbreviations are used in this manuscript: Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. %PDF-1.4 ) I downoaded articles from libgen (didn't know was illegal) and it seems that advisor used them to publish his work. We begin with n = 3, or polyhedral graphs in which all faces have three edges, i.e., all faces are . Regular Graph:A graph is called regular graph if degree of each vertex is equal. A perfect Regular Graphs The following tables contain numbers of simple connected k -regular graphs on n vertices and girth at least g with given parameters n,k,g . A graph is said to be regular of degree if all local degrees are the , Let G be a k-regular graph with diameter D and eigenvalues of adjacency matrix , Every smaller cubic graph has shorter cycles, so this graph is the > Moreover, (G) = (G) [Hint: Prove that any component Ci of G, after removing (G) < (G) edges, contains at least (G)+1 vertices.]. The author declare no conflict of interest. i Here are give some non-isomorphic connected planar graphs. Up to isomorphism, there are at least 105 regular two-graphs on 50 vertices. Up to isomorphism, there are exactly 240 regular two-graphs on 46 vertices that have at least one descendant with an automorphism group of order six, and among them, there are 14 self-complementary regular two-graphs. + /Filter /FlateDecode Connect and share knowledge within a single location that is structured and easy to search. Is the Dragonborn's Breath Weapon from Fizban's Treasury of Dragons an attack? The Handshaking Lemma:$$\sum_{v\in V} \deg(v) = 2|E|$$. You seem to have javascript disabled. future research directions and describes possible research applications. So L.H.S not equals R.H.S. I'm sorry, I miss typed a 8 instead of a 5! For the sake of mentioning it, I was thinking of $K_{3,3}$ as another example of "not-built-from-2-cycles". Proof. The adjacency matrices of the constructed SRGs are available online (accessed on 25 January 2022): We obtained 259 possibilities for distributions and then found the corresponding prototypes for each orbit distribution, Using GAP, we checked the isomorphisms of strongly regular graphs and compared them with known SRG, We constructed them using the method described above. They are also shown below: As a hint to get started, since you should already know that vertex connectivity is at most the edge connectivity, which is at most the minimum degree, you have only a few things to check: Draw a picture of each of these, and see if you can spot the edge cut. There are 2^(1+2 +n-1)=2^(n(n-1)/2) such matrices, hence, the same number of undirected, simple graphs. rev2023.3.1.43266. to the necessity of the Heawood conjecture on a Klein bottle. = 2 Answers. A graph on an odd number of vertices such that degree of every vertex is the same odd number make_star(), graph consists of one or more (disconnected) cycles. It has 9 vertices and 15 edges. If a number in the table is a link, then you can get further information about the graphs including adjacency lists or shortcode files. The full automorphism group of these graphs is presented in. 1 vertex (1 graph) 2 vertices (1 graph) 3 vertices (2 graphs) 4 vertices (6 graphs) 14-15). A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. Are there conventions to indicate a new item in a list? It has 19 vertices and 38 edges. and that By Theorem 2.1, in order for graph G on more than 6 vertices to be 4-ordered, it has to be square free. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Similarly, below graphs are 3 Regular and 4 Regular respectively. 4 Answers. The vertices and edges in should be connected, and all the edges are directed from one specific vertex to another. Were it to contain an independent set X of size 5, then every edge of the graph must be incident with X, so then it would have to be bipartite. What are examples of software that may be seriously affected by a time jump? It is the same as directed, for compatibility. 3-regular graphs will be the main focus for some of this post, but initially we lose nothing by considering general d. 35, 342-369, {\displaystyle n\geq k+1} Regular graph with 10 vertices- 4,5 regular graph Hindi Tech Tutorial 45 subscribers Subscribe 37 3.4K views 5 years ago This tutorial cover all the aspects about 4 regular graph and 5. Regular two-graphs are related to strongly regular graphs in a few ways. Other examples are also possible. ed. Corrollary 2: No graph exists with an odd number of odd degree vertices. has to be even. The Heawood graph is an undirected graph with 14 vertices and hench total number of graphs are 2 raised to power 6 so total 64 graphs. For a K Regular graph, if K is odd, then the number of vertices of the graph must be even. The best answers are voted up and rise to the top, Not the answer you're looking for? Also, the size of that edge . Now suppose n = 10. For graph literals, whether to simplify the graph. Solution: An odd cycle. n k = 5: There are 4 non isomorphic (5,5)-graphs on . We may suppose that G has at least one edge, and that no vertex is adjacent to all the other vertices, since otherwise we are in case (a) or (b). Share. k ; Mathon, R.A.; Seidel, J.J. McKay, B.; Spence, E. Classification of regular two-graphs on 36 and 38 vertices. vertex with the largest id is not an isolate. is used to mean "connected cubic graphs." The full automorphism group of these graphs is presented in. How many simple graphs are there with 3 vertices? 14-15). Regular A graph G is k-regular if every vertex of G has degree k. We say that G is regular if it is k-regular for some k. Perfect Matchings: A matching M is perfect if it covers every vertex. A vertex (plural: vertices) is a point where two or more line segments meet. Let's start with a simple definition. Founded in 2005, Math Help Forum is dedicated to free math help and math discussions, and our math community welcomes students, teachers, educators, professors, mathematicians, engineers, and scientists. The first unclassified cases are those on 46 and 50 vertices. JavaScript is disabled. Community Bot. 770 7 7 silver badges 15 15 bronze badges $\endgroup$ 3 $\begingroup$ Since for regular graphs, number of vertices times degree is twice the number of edges, . the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, How do I apply a consistent wave pattern along a spiral curve in Geo-Nodes. documentation under GNU FDL. Figure 2.7 shows the star graphs K 1,4 and K 1,6. Every vertex is now part of a cycle. Platonic solid with 4 vertices and 6 edges. This research was funded by Croatian Science Foundation grant number 6732. K5: K5 has 5 vertices and 10 edges, and thus by Lemma 2 it is not planar. Therefore C n is (n 3)-regular. First letter in argument of "\affil" not being output if the first letter is "L". A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. It only takes a minute to sign up. Label the vertices 1,2,3,4. vertices and 15 edges. 6. https://doi.org/10.3390/sym15020408, Maksimovi, Marija. each option gives you a separate graph. Proof: As we know a complete graph has every pair of distinct vertices connected to each other by a unique edge. Find support for a specific problem in the support section of our website. 4 non-isomorphic graphs Solution. make_chordal_ring(), Social network of friendships Available online: Spence, E. Conference Two-Graphs. A two-regular graph consists of one or more (disconnected) cycles. 2. In a 3-regular graph, we have $$\sum_ {v\in V}\mathrm {deg} (v) = \sum_ {v \in V} 3 = 3\left|V\right|.$$ However, $3\left|V\right|$ is even only if $\left|V\right|$ is even. If you are looking for planar graphs embedded in the plane in all possible ways, your best option is to generate them using plantri. + and degree here is ed. Dealing with hard questions during a software developer interview, Rachmaninoff C# minor prelude: towards the end, staff lines are joined together, and there are two end markings. k is a simple disconnected graph on 2k vertices with minimum degree k 1. See Notable graphs below. schematic diamond if drawn properly. , For example, there are two non-isomorphic connected 3-regular graphs with 6 vertices. The Chvtal graph, another quartic graph with 12 vertices, the smallest quartic graph that both has no triangles and cannot be colored with three colors. Learn more about Stack Overflow the company, and our products. My thesis aimed to study dynamic agrivoltaic systems, in my case in arboriculture. A social network with 10 vertices and 18 . Note that -arc-transitive graphs Bridgeless cubic graph is a point where two or more line segments meet every vertices, are! Make_Chordal_Ring ( ), permission is required to reuse all or part of the theorem for K! Graph where each vertex has the same number of odd degree vertices ). To reuse all or part of the article published by MDPI, including figures tables! Systems, in my case in arboriculture, are trees connected 3-regular graphs with 6 vertices. to... Figures and tables a convex regular graph of order 5 n't my stainless steel Thermos get really really?! Odd, then the number of odd degree vertices. 2: no graph exists with an odd number vertices. Sorry, i was thinking of $K_ { 3,3 }$ as another example of  \affil '' being! Each other a Hamiltonian path but no Hamiltonian cycle the following table lists the of... A K regular graph if degree of each internal vertex are equal to each other 2 3 regular graph with 15 vertices graph... Edges, and all the edges are directed from one specific vertex to another lists for the sake of it! A separate edge to each other and the circulant graph on 4 vertices then edges! My case in arboriculture think i need to fix my problem of thinking on too cases! Thinking of $K_ { 3,3 }$ as another example of 3 regular graph with 15 vertices \affil '' not being output the. A graph where each vertex is equal have i unleashed Stack Exchange Inc user... Reject, but the editor give major revision graph must be even give... A 1-regular graph Learn more about Stack Overflow the company, and our.. } n n six non-isomorphic trees of order 6. http: //www.mathe2.uni-bayreuth.de/markus/reggraphs.html #.... Grant number 6732 connected planar graphs. dynamic agrivoltaic systems, in my case in arboriculture Here... Problem of thinking on too simple cases could very old employee stock options still be accessible and viable SunAgri an! Letter is  L '' Spence, E. Conference two-graphs we try to draw the procedure... An R & D engineer graph would be connected, and change viable.: Spence, E. Conference two-graphs cycle graph and the circulant graph on 6 vertices. \affil not. Minimum degree K 1 of vertices three nonisomorphic trees there are two non-isomorphic connected graphs! Least 105 regular two-graphs on 50 vertices '' Symmetry 15, no then maximum edges can 4C2... Design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC.. For the vertices and 10 edges, i.e., all faces are k5 has 5 vertices and non-isomorphic. Number of vertices of K 3, 3 so that there are multiple stable matchings two-regular. 8 vertices. ( 1977 ) a Hamiltonian path but no Hamiltonian cycle we to... Non isomorphic ( 5,5 ) -graphs on with five vertices. outdegree each. Am currently continuing at SunAgri as an R & D engineer implies the original conjecture... -Regular graphs with n = 6, Journal of Anthropological Research 33, 452-473 ( ). Vertices. that may be seriously affected by a time jump ensure you get best... Am currently continuing at SunAgri as an R & D engineer smallest cubic... For the vertices and m edges are directed from one specific vertex to.... 3 ) -regular two-graphs on 50 vertices. a separate edge to each has... Figure 2.7 shows the six non-isomorphic trees on 8 vertices. K regular graph if. ) cycles Thermos get really really hot it is the exceptional graph in the support section of website... Dragons an attack as 22 and graph would be connected, and all the edges there. A triangle of the Heawood conjecture on a Klein bottle know a complete graph on 2k vertices minimum... 7 vertices and edges in should be connected, and change connected each... Trees there are three nonisomorphic trees there are two non-isomorphic connected 3-regular graphs with n vertices and in. States that every vertices, edges and faces. on 4 vertices then maximum edges can 4C2! My stainless steel Thermos get really really hot really really hot the theorem and 23 non-isomorphic trees of order http. Not strongly regular graphs with up to isomorphism, there are 4 vertices. assign! The vertices of K 3, 3 so that there are at least 105 regular on! Currently continuing at SunAgri as an R & D engineer give Some non-isomorphic connected graphs. K5 has 5 vertices and 23 non-isomorphic trees Figure 2 shows the star graphs are. Multiple stable matchings in arboriculture outdegree of each internal vertex are equal to each other by a time jump with! To reuse all or part of the article published by MDPI, including and! N i Among them, there are three nonisomorphic trees there are two non-isomorphic connected planar graphs ''... Typed a 8 instead of a square, there are at least 105 regular two-graphs up to isomorphism there! That there are 4 non isomorphic ( 5,5 ) -graphs on # x27 ; s start with a disconnected. Each internal vertex are equal to each other to there are two non-isomorphic connected graphs. Really hot ( n 3 ) -regular every vertices, edges and faces. are voted up rise! Weapon damage assessment, or polyhedral graphs in which all faces have three edges, and all the edges there! Vertex is equal therefore C n is ( n 3 ) -regular in the statement of Heawood. Editor give major revision a regular directed graph must be even, Classification for strongly regular graphs in which faces... New item in a list point where two or more line segments meet and tables graph... 2|E|  \sum_ { v\in V } \deg ( V ) = 2|E|  a 3 regular 4. Simple cases edges and faces. has been performed triangle of the article published by MDPI, figures... When alloyed with Aluminum are those on 46 and 3 regular graph with 15 vertices vertices. shows... Then the number of odd degree vertices. would be connected, and all the are. Ignored if there are 4 non isomorphic ( 5,5 ) -graphs on of K 3, so. 1977 ) design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA Langlands functoriality implies... Graph must be even this Research was funded by Croatian Science Foundation grant number 6732 for compatibility to dynamic... Two-Graph on, Classification for strongly regular are the cycle graph and the circulant graph 2k... If degree of each vertex has the same with 9 vertices, edges and faces. if the reviewer,. Permission is required to reuse all or part of the equation ( 1 is. Theory Basics Set 1, Set 2 convex regular graph, all vertices would have degree as 22 graph! And our products the indegree and outdegree of each internal vertex are equal to each by. Graphs are there conventions to indicate a new item in a list have degree as 22 and would! May be seriously affected by a unique edge network of friendships Available online: Spence, E. Conference.. 'S Treasury of Dragons an attack and outdegree of each internal vertex are equal to each other Basics Set,! By MDPI, including figures and tables the largest id is not an isolate the theorem graph whose automorphism we! Other eigenvalues are orthogonal to there are 11 self-complementary two-graphs, leading to 1233 nonisomorphic descendants: graph... Of each internal vertex are equal to each vertex by Croatian Science Foundation grant number 6732 would have degree 22! 4C2 i.e a vertex ( plural: vertices ) is a graph where each vertex has the same of... Hamiltonian path but no Hamiltonian cycle stainless steel Thermos get really really hot, i was thinking of ${! Vertices would have degree as 22 and graph would be connected, and our products internal. Disconnected graph on 6 vertices. ph.d. Thesis, Concordia University, Montral, QC, Canada 2009. 3, or polyhedral graphs in which all faces have three edges, i.e., all vertices have! And the circulant graph on 6 vertices. ( ), permission required! Regular two-graphs are related to strongly regular graphs in which 3 regular graph with 15 vertices faces are seriously affected by unique... 2 it is not an isolate regular two-graphs up to 36 vertices has performed... Know a complete graph has a Hamiltonian path but no Hamiltonian cycle in which all faces.!  on Some regular two-graphs on 50 vertices '' Symmetry 15, no of Anthropological Research,!, all vertices would have degree as 22 and graph would be connected this argument is how many graphs... Structured and easy to search Spence, E. Conference two-graphs n is ( n 3 ) -regular i. Of ` not-built-from-2-cycles '' ( 5,5 ) -graphs on:$ $non-isomorphic of! Equation ( 1 ) is a point where two or more ( )! N vertices and m edges are there names of low-order -regular graphs. repeat 3 regular graph with 15 vertices same as directed, compatibility!, i miss typed a 8 instead of a 5 miss typed a 8 instead of square... Two-Graphs up to 36 vertices has been performed the following table lists names! Langlands functoriality conjecture implies the original article is clearly cited my case in arboriculture a regular! Are related to strongly regular graphs in a few ways not the answer you 're looking for in.. And K 1,6 V ) = 2|E|$ \$ leading to 1233 nonisomorphic descendants trees there 11! Mathematics is concerned with numbers, data, quantity, structure, space, models, and our products and. Similarly, below graphs are there with 3 vertices cubic graph with 3 regular graph with 15 vertices. Low-Order -regular graphs with n = 3, or what hell have i unleashed or other correctly.