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| properties = [[Strongly regular graph|Strongly regular]]<br/>[[Symmetric graph]] The '''Suzuki graph''' is a [[strongly regular graph]] with parameters <math>(1782, 416, 100, 96)</math>. Its automorphis ...

{{Short description|Strongly regular graph}} | properties = [[Strongly regular graph|Strongly regular]]<br/>[[Symmetric graph]] ...

| properties = [[Strongly regular graph|Strongly regular]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Triangle-free graph|Triangle-fr ...ef>[http://genealogy.math.ndsu.nodak.edu/id.php?id=35587 Allan Gewirtz], ''Graphs with Maximal Even Girth'', Ph.D. Dissertation in Mathematics, City Universi ...

...nt–Seidel graph''' is a [[locally linear graph|locally linear]] [[strongly regular graph]] with parameters <math>(243,22,1,2)</math>. This means that it has 2 ...h]] of an [[abelian group]]. Among abelian Cayley graphs that are strongly regular and have the last two parameters differing by one, it is the only graph tha ...

*[[Strongly regular graph|strongly regular]] ...ph theory]], the '''Brouwer&ndash;Haemers graph''' is a 20-[[regular graph|regular]] [[undirected graph]] with 81 vertices and 810 edges. ...

...|locally linear]] [[strongly regular graph]]. Its parameters as a strongly regular graph are (729,112,1,20). This means that it has 729 vertices, and 40824 ed ...such extra triangle can exist. The remaining property of strongly regular graphs, that all non-adjacent pairs of points have the same number of shared neigh ...

{{Short description|On existence of a strongly regular graph}} {{unsolved|mathematics|Does there exist a [[strongly regular graph]] with parameters (99,14,1,2)?}} ...

| properties = [[Strongly regular graph|Strongly regular]]<br>[[Claw-free graph|Claw-free]]<br>[[Hamiltonian path|Hamiltonian]] ...]] [[undirected graph]] with 27 vertices and 216 edges. It is a [[strongly regular graph]] with parameters srg(27,&thinsp;16,&thinsp;10,&nbsp;8). ...

...stance), and asked for a characterization of them.{{r|ore}} Although these graphs can be recognized in [[polynomial time]], "more than sixty years later a fu ...en1 tiny.svg|thumb|upright=0.6|The [[Petersen graph]], one of the geodetic graphs of diameter two]] ...

{{Short description|One of two different regular graphs with 16 vertices}} | properties = [[Strongly regular graph|Strongly regular]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Cayley graph]]<br>[[Vertex-tran ...

...st in an undirected graph, the graph must be connected and [[regular graph|regular]] of even [[degree (graph theory)|degree]]. A directed graph with such a decomposition must be [[strongly connected graph|strongly connected]] and all vertices must have the same in-degree and out-degree as ...

[[File:Frucht graph.dot.svg|thumb|The [[Frucht graph]], a 3-[[regular graph|regular]] graph whose automorphism group realizes the [[trivial group]].]] ...ism|non-isomorphic]] [[simple graph|simple]] [[connected graph|connected]] graphs such that the [[automorphism group]] of each of them is [[group isomorphism ...

{{for|related notion (also called cycle rank) in undirected graphs|circuit rank}} ...st is acyclic, being a DAG, so has a cycle rank of 0. The second and third graphs have the same cycle rank, because there is a point in each where, if remove ...

...uare. It is a [[toroidal graph]], a [[locally linear graph]], a [[strongly regular graph]] with parameters (9,4,1,2), the <math>3\times 3</math> [[rook's grap ...e graph of a 3-3 duoprism may be ascertained by the [[Cartesian product of graphs]] between two identical both [[complete graph]]s <math> K_3 </math>.{{r|che ...

...}}.</ref> Pancyclic graphs are a generalization of [[Hamiltonian graph]]s, graphs which have a cycle of the maximum possible length. ==Planar graphs== ...

...l.svg|thumb|The polyhedral graph formed as the [[Schlegel diagram]] of a [[regular dodecahedron]].]] ...lyhedron]]. Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the [[k-vertex-connected graph|3-vertex-connected]], [[planar graph]]s. ...

{{Short description|Bipartite 4-regular graph with 20 nodes and 40 edges}} *[[regular graph|Regular]] ...

...[[Steiner system|partial Steiner triple systems]], and the locally linear graphs are exactly the [[Gaifman graph]]s of these hypergraphs or partial Steiner ...r locally linear graphs. Certain [[Kneser graph]]s, and certain [[strongly regular graph]]s, are also locally linear. ...

| name = 3-regular girth-5 matchstick graph ...is reason, matchstick graphs have also been called '''planar unit-distance graphs'''.<ref>{{citation ...

...mplete bipartite graph]] on the same vertices. The name was given to these graphs by [[Paul Erdős]] and [[András Hajnal]].{{r|e}} The same concept can also be defined in the same way for infinite graphs over two copies of any ordered set of vertices.{{r|e}} ...