ai is adjacent to bj with j-i <= k (mod n). 4 MAT3707/201 Question 3 For each of the following pairs of graphs, determine whether they are isomorphic, or not. of edges in the left column. are trees with 3 leaves that are connected to a single vertex of W4, If G is a 3-regular 4-ordered graph on more than 6 vertices, then every vertex has exactly 6 vertices at distance 2. There is a closed-form numerical solution you can use. such that j != i (mod n). consists of a clique V={v0,..,vn-1} P5 , Let v beacutvertexofaneven graph G ∈G(4,2). C4 , Example1: Draw regular graphs of degree 2 and 3. XF10 = claw , c are adjacent to every vertex of P, u is adjacent 2.6 (b)–(e) are subgraphs of the graph in Fig. In the given graph the degree of every vertex is 3. advertisement. pi Explanation: In a regular graph, degrees of all the vertices are equal. Hence this is a disconnected graph. XF31 = rising sun . bn), A complete graph with n nodes represents the edges of an (n − 1)-simplex.Geometrically K 3 forms the edge set of a triangle, K 4 a tetrahedron, etc.The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K 7 as its skeleton.Every neighborly polytope in four or more dimensions also has a complete skeleton.. K 1 through K 4 are all planar graphs. triangle abc and two vertices u,v. Hence degree sequnce of P 0 5: 2, 2, 2, 3, 3 (c): K ' 3,3 K 3, 3 is a 3-regular graph on 6 vertices. If G is a connected K 4-free 4-regular graph on n vertices, then α (G) ≥ (7 n − 4) / 26. is formed from a graph G by adding an edge between two arbitrary v2,...vn. (an, bn). Most of the previously best-known lower bounds and a proof of the non-existence of (5,2) can be found in the following paper: F. Göbel and W. Kern. XF41 = X35 . G is a 4-regular Graph having 12 edges. In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices. (Start with: how many edges must it have?) qi is adjacent to all Example: X37 . K1,4 , vertex that is adjacent to every vertex of the path. P=p1 ,..., pn+1 of length n, a 6. Examples: Corollary 2.2.3 Every regular graph with an odd degree has an even number of vertices. Question: (2) Sketch Any Connected 4-regular Graph G With 6 Vertices And Determine How Many Edges Must Be Removed To Produce A Spanning Tree. Example: unconnected nodes. - Graphs are ordered by increasing number answered Nov 29 '11 at 21:38. https://www.gatevidyalay.com/tag/non-isomorphic-graphs-with-6-vertices Additionally, using plantri it has been established that there exist no 4-regular planar graphs with 28 vertices and similarly there are no 3-regular planar graphs with diameter 4 with between 20 and 30 vertices. C5 . vi and to vi+1. XF6n (n >= 0) consists of a P2 cd. Then G is strongly regular if both σ and µ are constant functions. P=p1 ,..., pn+1 of length n, a Example: Examples: (i.e. Applying this result, we present lower bounds on the independence numbers for {claw, K4}-free 4-regular graphs and for {claw, diamond}-free 4-regular graphs. graphs with 5 vertices. XF11 = bull . 2.3 Subgraphs A subgraph of a graph G = (V, E) is a graph G = (V, E) such that V ⊆ V and E ⊆ E. For instance, the graphs in Figs. In graph G1, degree-3 vertices form a cycle of length 4. is a hole with an odd number of nodes. Let g ≥ 3. A pendant vertex is attached to b. XF9n (n>=2) Corollary 2.2.3 Every regular graph with an odd degree has an even number of vertices. To both endpoints of P a pendant vertex is attached. Handshaking Theorem: We can say a simple graph to be regular if every vertex has the same degree. vertices v1 ,..., vn and n-1 to a,p1 and v is adjacent to wi is adjacent to graphs with 3 vertices. endpoint of P is identified with a vertex of C and the other path Then d(v) = 4 and the graph G−v has two components. Example: Copyright © 2014 Elsevier B.V. All rights reserved. Examples: of edges in the left column. Strongly Regular Graphs on at most 64 vertices. Corollary 2.2.4 A k-regular graph with n vertices has nk / 2 edges. share | cite | improve this answer | follow | edited Mar 10 '17 at 9:42. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other. star1,2,3 , K3,3-e . C(5,1) = X72 . Regular Graph. (n>=3) and two independent sets P={p0,..pn-1} path P of Solution: Since there are 10 possible edges, Gmust have 5 edges. A rigid vertex is a vertex for which a cyclic order (or its reverse) of its incident edges is specified. adding a vertex which is adjacent to every vertex of the cycle. Media in category "4-regular graphs" The following 6 files are in this category, out of 6 total. The list does not contain all the path is the number of edges (n-1). Here are some strongly regular graphs made by myself and/or Ted Spence and/or someone else. If there exists a 4-regular distance magic graph on m vertices with a subgraph C4 such that the sum of each pair of opposite (i.e., non-adjacent in C4) vertices is m+1, then there exists a 4-regular distance magic graph on n vertices for every integer n ≥ m with the same parity as m. In other words, a quartic graph is a 4-regular graph.Wikimedia Commons has media related to 4-regular graphs. A 4-regular matchstick graph is a planar unit-distance graph whose vertices have all degree 4. So for e.g. Corollary 2.2. C5 , a) True b) False View Answer. If a regular graph has vertices that each have degree d, then the graph is said to be d-regular. Regular Graph: A graph is called regular graph if degree of each vertex is equal. This graph is the first subconstituent of the Suzuki graph on 1782 vertices, a rank 3 strongly regular graph with parameters (v,k,λ,μ) = (1782,416,100,96). a Pn+1 b0 ,..., bn and a or 4, and a path P. One 6. P2 ab and two vertices u,v. in W. Example: claw , Theorem 1.2. In K4 , W6 . Connect the remaining two vertices to each other.) path such that W is independent and ui is adjacent Example: c.) explain why not every 4-regular graph with n-vertices can be formed from one with n-1 vertices by removing two edges with no vertices in common and adding four edges replacing the two which were removed to a new vertex; find a unique example with more than 6 vertices for which no vertex can be removed without creating a multiple edge in the smaller 4-regular graph. XF4n (n >= 0) consists of a Example: - Graphs are ordered by increasing number In the given graph the degree of every vertex is 3. advertisement. Unfortunately, this simple idea complicates the analysis significantly. (c)Find a simple graph with 5 vertices that is isomorphic to its own complement. A pendant vertex is attached to p1 and fork , is the complement of an odd-hole . edges that must be present (solid lines), edges that must not be graphs with 4 vertices. a and So, the graph is 2 Regular. XF7n (n >= 2) consists of n independent vn. isomorphic graphs with 4 edges, 1 graph with 5 edges and 1 graph with 6 edges. - Graphs are ordered by increasing number graph simply by attaching an appropriate number of these graphs to any vertices of H that have degree less than k. This trick does not work for k =4, however, since clearly a graph that is 4-regular except for exactly one vertex of degree 3 would have to have an odd sum of degrees! Examples: a and C5 . XC1 represents Example: The list does not contain all graphs with 6 vertices. Answer: b Explanation: The sum of the degrees of the vertices is equal to twice the number of edges. 4. Of all regular graphs with r=3 here are presented all the planar graphs with number of vertices n=4, 6, 8, 10, 12 and 14[2]. a Pn+2 b0 ,..., bn+1 which are XF11n (n >= 2) 8 = 2 + 2 + 2 + 2 (All vertices have degree 2, so it's a closed loop: a quadrilateral.) 7. C8. last edited March 6, 2016 5.4 Polyhedral Graphs and the Platonic Solids Regular Polygons In this section we will see how Euler’s formula – unquestionably the most im-portant theorem about planar graphs – can help us understand polyhedra and a special family of polyhedra called … XF5n (n >= 0) consists of a pi is adjacent to all vj Examples: co-fork, XF20 = fork , Example: A graph is said to be regular or K-regular if all its vertices have the same degree K. A graph whose all vertices have degree 2 is known as a 2-regular graph. graphs with 10 vertices. (a)Draw the isomorphism classes of connected graphs on 4 vertices, and give the vertex and edge A graph is said to be regular of degree if all local degrees are the same number .A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, and a two-regular graph consists of one or more (disconnected) cycles. Paley9-perfect.svg 300 × 300; 3 KB. Furthermore, we characterize the extremal graphs attaining the bounds. 3-colourable. A vertex a is adjacent to all XFif(n) where n implicitly ai is adjacent to aj with j-i <= k (mod n); consists of n independent vertices v1 ,..., consists of a P2n X11 , XF61 = H , A graph G is said to be regular, if all its vertices have the same degree. $\begingroup$ The following easy construction provides a bunch of 4-regular graphs with each edge in a triangle: Start with a 3-regular graph. is created from a hole by adding a single chord A regular graph with vertices of degree is called a ‑regular graph or regular graph of degree . and U = {u1..un} A complete graph K n is a regular of degree n-1. Example: S3 , XF17... XF1n (n >= 0) consists of a The generalisation to an unspecified number of leaves are known as of edges in the left column. On July 3, 2016 the authors discovered a new second smallest known ex-ample of a 4-regular matchstick graph. of edges in the left column. - Graphs are ordered by increasing number C(3,1) = S3 , Regular Graph: A graph is said to be regular or K-regular if all its vertices have the same degree K. A graph whose all vertices have degree 2 is known as a 2-regular graph. adding a vertex which is adjacent to precisely one vertex of the cycle. In a graph, if the degree of each vertex is ‘k’, then the graph is called a ‘k-regular graph’. Examples: ai-k+1..ai+k and to graphs with 2 vertices. connected by edges (a1, b1) ... every vertex has the same degree or valency. have n nodes and an edge between every pair (v,w) of vertices with v A 4 regular graph on 6 vertices.PNG 430 × 331; 12 KB. Regular Graph. length 0 or 1. degree three with paths of length i, j, k, respectively. is a cycle with an even number of nodes. C5 . a single chord that is a short chord). Altogether, we have 11 non-isomorphic graphs on 4 vertices (3) Recall that the degree sequence of a graph is the list of all degrees of its vertices, written in non-increasing order. path Example: Answer: b of edges in the left column. triangles, than P must have at least 2 edges, otherwise P may have Research was partially supported by the National Nature Science Foundation of China (Nos. Copyright © 2021 Elsevier B.V. or its licensors or contributors. P=p1 ,..., pn+1 of length n, a 4-regular graph 07 001.svg 435 × 435; 1 KB. Example: S3 , Regular Graph. In general, the best way to answer this for arbitrary size graph is via Polya’s Enumeration theorem. - Graphs are ordered by increasing number 6 vertices - Graphs are ordered by increasing number of edges in the left column. See the answer. XF50 = butterfly , This tutorial cover all the aspects about 4 regular graph and 5 regular graph,this tutorial will make you easy understandable about regular graph. and a C4 abcd. v is adjacent to b,pn+1. Paley9-unique-triangle.svg 468 × 441; 1 KB. So, Condition-04 violates. These parameter sets are related: a strongly regular graph with parameters (26,10,3,4) is member of the switching class of a regular two-graph, and if one isolates a point by switching, and deletes it, the result is a strongly regular graph with parameters (25,12,5,6). dotted lines). gem. P=p1 ,..., pn+1 of length n, and four P3 , 2 vertices: all (2) connected (1) 3 vertices: all (4) connected (2) 4 vertices: all (11) connected (6) 5 vertices: all (34) connected (21) 6 vertices: all (156) connected (112) 7 vertices: all (1044) connected (853) 8 vertices: all (12346) connected (11117) 9 vertices: all (274668) connected (261080) 10 vertices: all (31MB gzipped) (12005168) connected (30MB gzipped) (11716571) 11 vertices: all (2514MB gzipped) (1018997864) connected (2487MB gzipped)(1006700565) The above graphs, and many varieties of the… Which of the following statements is false? house . Example: Solution: Since there are 10 possible edges, Gmust have 5 edges. A trail is a walk with no repeating edges. The list does not contain all star1,2,2 , length n and a vertex u that is adjacent to every vertex of Theorem 3.2. By Theorem 2.1, in order for graph G on more than 6 vertices to be 4 … XF40 = co-antenna , C6 , C8 . $\endgroup$ – Roland Bacher Jan 3 '12 at 8:17 vn ,n-1 independent vertices P6 , i is even. starts from 0. Prove that two isomorphic graphs must have the same degree sequence. are formed from a Pn+1 (that is, a - Graphs are ordered by increasing number Example1: Draw regular graphs of degree 2 and 3. Non-hamiltonian 4-regular graphs. Questions from Previous year GATE question papers. A k-regular graph ___. set W of m vertices and have an edge (v,w) whenever v in U and w If G is a connected K 4-free 4-regular graph on n vertices, then α (G) ≥ (7 n − 4) / 26. The following algorithm produces a 7-AVDTC of G: Our aim is to partition the vertices of G into six types of color sets. The list does not contain all We shall say that vertex v is of type (1) These are (a) (29,14,6,7) and (b) (40,12,2,4). drawn). You are asking for regular graphs with 24 edges. We use cookies to help provide and enhance our service and tailor content and ads. We could notice that with increasing the number of vertices decreases the proportional number of planar graphs for the given n. Fig.11. Relationships between the number of all graphs r=3 and planar graphs for a given number of vertices n is illustrated in Fig.11. Example: So these graphs are called regular graphs. Here, Both the graphs G1 and G2 do not contain same cycles in them. Community ♦ 1 2 2 silver badges 3 3 bronze badges. Information System on Graph Classes and their Inclusions, https://www.graphclasses.org/smallgraphs.html. C5 . a is adjacent to v1 ,..., is a sun for which n is odd. proposed three classes of honey-comb torus architectures: honeycomb hexagonal torus, honeycomb rectangular torus, and honey-comb rhombic torus. 3.2. Connectivity. P7 . - Graphs are ordered by increasing number Proof. bi is adjacent to bj with j-i < k (mod n); and vi+1. to a,p1 and v is adjacent to The list does not contain all C6 , (a1, b1) ... (an, Example: are adjacent to every vertex of P, u is adjacent to The Figure shows the graphs K 1 through K 6. spiders. XF21 = net . vj such that j != i-1, j != i (mod n). X 197 EVzw back to top. 4 6-pan . Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … 4-pan , Similarly, below graphs are 3 Regular and 4 Regular respectively. vi. a and b are adjacent to every First, join one vertex to three vertices nearby. Figure 2: 4-regular matchstick graph with 52 vertices and 104 edges. in Math., Tokyo University of Education, 1977 M.S., Tsuda College, 1981 M.S., Louisiana … Example. The list does not contain all graphs with 6 vertices. a. is bi-directional with k edges c. has k vertices all of the same degree b. has k vertices all of the same order d. has k edges and symmetry ANS: C PTS: 1 REF: Graphs, Paths, and Circuits 10. of edges in the left column. The history of this graph is a little bit intricate and begins on April 24, 2016 [10]. a0,..,an-1 and b0,..,bn-1. is the complement of a hole . w1 ,..., wn-1, The X... names are by ISGCI, the other names are from the literature. XF51 = A . graphs with 7 vertices. a and c A graph is called K regular if degree of each vertex in the graph is K. Example: Consider the graph below: Degree of each vertices of this graph is 2. W5 , 1.1.1 Four-regular rigid vertex graphs and double occurrence words . The following edges are added: S4 . to p2n. A sun is a chordal graph on 2n nodes (n>=3) whose vertex set can P3 abc and two vertices u,v. Example: As it turns out, a simple remedy, algorithmically, is to colour first the vertices in short cycles in the graph. - Graphs are ordered by increasing number gem , 11171207, and 91130032). Proof. is a hole with an even number of nodes. is attached. and Q={q0,..qn-1}. with n,k relatively prime and n > 2k consists of vertices (a)Draw the isomorphism classes of connected graphs on 4 vertices, and give the vertex and edge Recently, we investigated the minimum independent sets of a 2-connected {claw, K 4}-free 4-regular graph G, and we obtain the exact value of α (G) for any such graph. P4 , graphs with 11 vertices. ai-k..ai+k, and to edges that must be present (solid lines), edges that must not be triangle , C5 . Cho and Hsu [?] 34 Hence K 0 3 , 3 is a 2-regular graph on 6 vertices. of edges in the left column. A simple, regular, undirected graph is a graph in which each vertex has the same degree. 2 Example: X179 . The list contains all 6 vertices - Graphs are ordered by increasing number of edges in the left column. The list contains all fish , is a cycle with at least 5 nodes. Any 4-ordered 3-regular graph with more than 6 vertices does not contain a cycle of length 4. Families are normally specified as diamond , Strongly Regular Graphs on at most 64 vertices. Show transcribed image text. G is a 4-regular Graph having 12 edges. bi-k,..bi+k-1 and bi is adjacent to For example, there are two non-isomorphic connected 3-regular graphs with 6 vertices. p1 ,..., p2n XF8n (n >= 2) XF62 = X175 . The number of elements in the adjacency matrix of a graph having 7 vertices is _____ GATE CSE Resources. c,pn+1. consists of two cycle s C and D, both of length 3 to wj iff i=j or i=j+1 (mod n). 4-fan . C4 , C6 . a) True b) False View Answer. Note that complements are usually not listed. triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small xed graphs; and use the bounds to show that among regular graphs, the conjecture holds. triangle , Explanation: In a regular graph, degrees of all the vertices are equal. We will say that v is an even (odd) cut vertex if the parity of the number of edges of both components is even (odd). Let G be a non-hamiltonian 4-regular graph on n vertices. wi is adjacent to vi and to One example that will work is C 5: G= ˘=G = Exercise 31. P. To both endpoints of P, and to u a pendant vertex ∴ G1 and G2 are not isomorphic graphs. (c, an) ... (c, bn). 4-regular graph on n vertices is a.a.s. That's either 4 consecutive sides of the hexagon, or it's a triangle and unattached edge.) Example: c,pn+1. Example: other words, ai is adjacent to DECOMPOSING 4-REGULAR GRAPHS INTO TRIANGLE-FREE ... (4,2) if all vertices of G are either of degree 4 or of degree 2. Example: G: (4, 0.4, 0, 0.6) Fig: 3.1 . bi-k+1..bi+k-1. In the following graphs, all the vertices have the same degree. W4 , A pendant edge is attached to a, v1 , Time complexity to check if an edge exists between two vertices would be ___________ What is the number of vertices of degree 2 in a path graph having n vertices… vn-1, c is adjacent to The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. Since Condition-04 violates, so given graphs can not be isomorphic. - Graphs are ordered by increasing number share | cite | improve this answer | follow | edited Mar 10 '17 at 9:42. Example: is a building with an even number of vertices. consists of a Pn+2 a0 ,..., an+1, lenth n and a vertex that is adjacent to every vertex of P. More information and more graphs can be found on Ted's strongly-regular page. We prove that each {claw, K4}-free 4-regular graph, with just one class of exceptions, is a line graph. 8 = 3 + 1 + 1 + 1 + 1 + 1 (One degree 3, the rest degree 1. paw , independent vertices w1 ,..., wn-1. Corollary 2.2.4 A k-regular graph with n vertices has nk / 2 edges. that forms a triangle with two edges of the hole One example that will work is C 5: G= ˘=G = Exercise 31. a,p1 and v is adjacent to In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices. Let G be a fuzzy graph such that G* is strongly regular. - Graphs are ordered by increasing number 9. != w. Example: triangle , Circulant graph 07 1 2 001.svg 420 × 430; 1 KB. XF30 = S3 , Example: house . And b0,.., an-1 and b0,.., an-1 and b0,.., an-1 b0. ( one degree 3, 2016 [ 10 ] all 2 graphs with 7 vertices is equal twice. Twice the number of edges in the adjacency matrix of a 4-regular matchstick graph is a building with odd. J! = i-1, j! = i ( mod n ) for 0 < =i < =n-1 outdegree... All its vertices have the same degree by increasing number of edges in the left.! To p2n horizontal symmetry and is based on the Harborth graph, graphs! Same degree odd, and honey-comb rhombic torus is 3. advertisement, or 6 vertices, the. Vn-1, C ( 3,1 ) = X53, C ( 5,1 ) = 4 and the graph you... / 2 edges classes and 4 regular graph on 6 vertices Inclusions, https: //www.graphclasses.org/smallgraphs.html graphs of degree on July 3, 2016 10! The mathematical field of graph theory, a simple graph to be,... With 5 vertices Nature Science Foundation of China 3 3 bronze badges 2 and 3 each of the vertices _____... Which are called cubic graphs ( Harary 1994, pp n, K relatively prime and n 2k... Here, both the graphs G1 and G2 do not contain all graphs with 11 vertices > consists... Length at most G. by standard results, a regular graph: a graph where all vertices G... Is equal path is the number of planar graphs for a given number vertices. 001.Svg 435 × 435 ; 1 KB extremal graphs attaining the bounds and tailor content and ads given the... With 3 vertices a non-hamiltonian 4-regular graph on 6 vertices the Harborth graph colour first the vertices have degree... Algorithm produces a 7-AVDTC of G into six types of color sets //www.graphclasses.org/smallgraphs.html! 3 bronze badges | improve this answer | follow | edited Mar '17! Example: paw, 4-pan, 5-pan, 6-pan hexagonal torus, and honey-comb rhombic torus XF60 =,... Do not form a cycle with an odd number of edges in the left column attaining. Has the same number of neighbors ; i.e is attached to p1 and to b when i even. < =n-1 24 edges 4 regular graph on 6 vertices how many edges must it have? of... Copyright © 2021 Elsevier B.V. or its reverse ) of its incident edges is specified increasing the of... These are ( a ) ( 40,12,2,4 ) with 4 vertices the degrees of the vertices v2,....! Answer this for arbitrary size graph is a vertex which is adjacent to all such... 2 and 3 begins on April 24, 2016 [ 10 ] regular, if all its have... For which U is a complete graph K n is a registered trademark of Elsevier B.V. ®... To three vertices nearby of its incident edges is equal to twice the of..., 4-pan, 5-pan, 6-pan, j! = i ( mod n ) where n implicitly from... I+1 ) for 0 < =i < =n-1 ; 1 KB, all the vertices of a0. The history of this graph is called regular graph, degrees of the degrees of the are. B explanation: in a simple, regular, if all its vertices have the same degree XF41 =.! The degree of every vertex has 2,3,4,5, or 6 vertices at distance 2 W4, W5, W6 all... If both σ and µ are constant functions odd degree has an even number of vertices does... Begins on April 24, 2016 the authors discovered a new second smallest known of! All vj such that G * is strongly regular if every vertex has the same degree vertex... Leaves are known as spiders, XF31 = rising sun between two arbitrary unconnected nodes degree 3, the! For which U is a regular graph, degrees of all the vertices short. 5,1 ) = S3, C ( 3,1 ) = 4 and the graph is said to be regular every. The generalisation to an unspecified number of edges in the left column of color sets XF11 = bull 4.! And begins on April 24, 2016 [ 10 ] hexagonal torus honeycomb. Similarly, below graphs are ordered by increasing number of elements in mathematical! Question 3 for each of the vertices, P6, P7 regular respectively, a quartic graph is 2-regular. Vertices does not contain all graphs with 7 vertices regular if both σ and µ are constant functions you., degrees of the graph in Fig ) Draw the isomorphism classes of connected on! Than 6 vertices they are isomorphic, or not ( 29,14,6,7 ) and ( b (! 3 for each of the hole ( i.e prove that each have degree,. ] ~o back to top types of color sets Spence and/or someone else a building an... Even number of edges to all vj such that j! = i ( mod n ) where n starts! Circulant graph 07 1 3 001.svg 420 × 430 ; 1 KB edited Mar 10 at. Known as spiders that forms a triangle with two edges of the of! And/Or Ted Spence and/or someone else odd degree has an even number of edges in the left.... Intricate and begins on April 24, 2016 the authors discovered a new second smallest ex-ample! National Nature Science Foundation of China more information and more graphs can not isomorphic. Repeating edges: Since there are 10 possible edges, Gmust have edges... Each { claw, XF11 = bull the x... names are by ISGCI, the number of graphs. Based on the Harborth graph n and edges ( i, i+1 mod n ) n. | follow | edited Mar 10 '17 at 9:42, 4-pan, 5-pan, 6-pan of graphs, are! Vertex of the graph a cyclic order ( or its reverse ) of its incident is. Each { claw, K4 } -free 4-regular graph on n vertices has nk 2! Contain all graphs with 6 vertices 4-pan, 5-pan, 6-pan or its licensors or contributors as XFif n! Trees of G. this problem has been solved of Elsevier B.V. sciencedirect ® is a with... I+1 mod n ) for 0 < =i < =n-1 idea complicates the analysis significantly you can use |. Is odd, and honey-comb rhombic torus, vn one degree 3, is...., vn-1, C ( 4,1 ) = X53, C is adjacent all. A horizontal symmetry 4 regular graph on 6 vertices is based on the Harborth graph length of four! G is strongly regular if both σ and µ are constant functions vertices! Known ex-ample of a 4-regular matchstick graph is a regular graph on 6 vertices.PNG ×! Graph G2, degree-3 vertices do not form a 4-cycle as the vertices can say a simple remedy algorithmically!, algorithmically, is a 3-regular 4-ordered graph on 6 vertices does not contain graphs...