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...hnique in radio frequency engineering|Smith chart|the Biggs–Smith distance-regular graph|Biggs–Smith graph}} ...e=42 |pages=19–40 |last1=Cvetković |first1=Dragoš |year=2017 }}</ref> The graphs with spectral radius 2 form two infinite families and three sporadic exampl ...

| properties = [[Strongly regular graph|Strongly regular]]<br>[[Vertex-transitive graph|Vertex-transitive]]<br>[[Cayley graph]]<br>[ ...', also known as the '''Hall-Janko-Wales graph''', is a 36-[[regular graph|regular]] [[undirected graph]] with 100 vertices and 1800 edges.<ref>{{MathWorld | ...

.... every vertex has the same [[Degree (graph theory)|degree]] or valency. A regular [[directed graph]] must also satisfy the stronger condition that the [[inde ...degree {{mvar|k}} is called a '''{{nowrap|{{mvar|k}}‑regular}} graph''' or regular graph of degree {{mvar|k}}. ...

...strongly connected components of a graph", or the definition of connected graphs has to be modified not to include {{math|''K''{{sub|0}}}}). To avoid the ne ...]], the order-zero graph is, according to some definitions of "category of graphs," the [[initial object]] in the category. ...

...ngly regular graph]]s, and also [[finite group]]s because many regular two-graphs have interesting [[automorphism group]]s. ...lled '''2-graphs''' in [[graph theory]], such as [[regular graph|2-regular graphs]]. ...

...nsitive graph|distance-transitive]], and [[distance-regular graph|distance-regular]]. It has [[Diameter (graph theory)|diameter]] 2. Its [[Graph automorphism ...a]]ic methods are applied to problems about [[Graph (discrete mathematics)|graphs]]. This is in contrast to [[geometric graph theory|geometric]], [[combinato ...

...nearity graph]]) of a <math>\mathrm{pg}(s,t,\alpha)</math> is a [[strongly regular graph]]: {{tmath|1= \mathrm{srg}\Big((s+1)\frac{(s t+\alpha)}{\alpha},s(t+1 ...be easily shown that the collinearity graph of such a geometry is strongly regular with parameters ...

==Examples and types of graphs== * [[Distance regular graph]] ...

...:Paley13.svg|thumb|upright=1.1|The [[Paley graph]] of order 13, a strongly regular graph with parameters {{math|(13,6,2,3)}}.]] In [[graph theory]], a '''strongly regular graph''' ('''SRG''') is a [[regular graph]] {{math|1=''G'' = (''V'', ''E'')}} with {{mvar|v}} vertices and [[De ...

...; each vertex has degree <math>n-q-1</math> or <math>n-q</math>. It is a [[regular graph]] if <math>n</math> is divisible by <math>r</math> (i.e. when <math>s Turán graphs are named after [[Pál Turán]], who used them to prove Turán's theorem, an i ...

{{Short description|Class of undirected graphs defined from systems of sets}} | properties = [[Regular graph|<math>k(n-k)</math>-regular]]<br/>[[Vertex-transitive graph|Vertex-transitive]]<br/>[[Distance-transiti ...

{{unsolved|mathematics|Are graphs uniquely determined by their subgraphs?}} Informally, the '''reconstruction conjecture''' in [[graph theory]] says that graphs are determined uniquely by their subgraphs. It is due to [[Paul Kelly (mat ...

| title = On the Graphs of Hoffman&ndash;Singleton and Higman&ndash;Sims | properties = [[Strongly regular graph|Strongly regular]]<br>[[Edge-transitive graph|Edge-transitive]]<br>[[Hamiltonian graph|Hamil ...

| properties = [[Strongly regular graph|Strongly regular]]<br>[[Conference graph]]<br>[[Self-complementary graph|Self-complementary] ...inite family of symmetric [[conference matrix|conference matrices]]. Paley graphs allow [[graph-theoretic]] tools to be applied to the [[number theory]] of q ...

{{Short description|7-regular undirected graph with 50 nodes and 175 edges}} | properties = [[Strongly regular graph|Strongly regular]]<br/>[[Symmetric graph|Symmetric]]<br/>[[Hamiltonian graph|Hamiltonian]]<b ...

{{distinguish|text = the [[Heawood graphs]], a graph family that contains the Heawood graph}} ...ransitive graph|Distance-transitive]]<br>[[Distance-regular graph|Distance-regular]]<br>[[Toroidal graph|Toroidal]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[ ...

...ath]]. This definition is equivalent to the topological one, as applied to graphs, but it is easier to deal with in the context of [[graph theory]]. Graph th ...another example, a [[directed graph]] is ''[[strongly connected component|strongly connected]]'' if each [[ordered pair]] of vertices is joined by a [[directe ...

...-vertex-critical'' if each of its vertices is a critical element. Critical graphs are the ''minimal'' members in terms of chromatic number, which is a very i ...hat is, every vertex is adjacent to at least <math>k-1</math> others. More strongly, <math>G</math> is <math>(k-1)</math>-[[K-edge-connected graph|edge-connect ...

...The star height of a regular ''language'' is the least star height of any regular expression for that language. ...formally, the star height of a [[Regular expression#Formal language theory|regular expression]] ...

==Graphs== There are two interesting graphs that can be obtained from a generalized quadrangle. ...