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...ast1=Babai |first1=László |authorlink=László Babai|title=Spectra of Cayley graphs |journal=[[Journal of Combinatorial Theory, Series B]] |date=October 1979 | ...he [[Cayley graph]] (or [[Lovász conjecture#Directed Cayley graph|directed Cayley graph]]) corresponding to a [[Generating set of a group|generating subset]] ...

...Like the <math>9\times 9</math> [[Sudoku graph]] it is an integral abelian Cayley graph whose group elements all have order 3, one of a small number of possi ...} [[Conway's 99-graph problem]] concerns the existence of another of these graphs, the one with parameters <math>(99,14,1,2)</math>.{{r|con}} ...

...ayley graph | Cayley graphs]], in particular, [[circulant graph |circulant graphs]], and many of their decompositions come from the action of a [[permutation ...

...more general classes of algebraic groups ''G'', is that the sequence of [[Cayley graph]]s for reductions Γ_''p'' modulo prime numbers ''p'', with ...en ''p'' is large enough), or that the locally constant functions on these graphs are constant, so that the eigenspace for the first eigenvalue is one-dimens ...

Although bouquets have a very simple structure as graphs, they are of some importance in [[topological graph theory]] because their ...p theory]], every [[Cayley graph|Cayley–Serre graph]] (a variant of Cayley graphs with doubled edges) can be represented as the [[covering graph]] of a bouqu ...

| properties = [[Cayley graph]]<br>[[Symmetric graph|Symmetric]]<br>[[Cubic graph|Cubic]]<br>[[Hami ...COND">[[Marston Conder|Conder, M.]] and Dobcsányi, P. "Trivalent Symmetric Graphs Up to 768 Vertices." J. Combin. Math. Combin. Comput. 40, 41&ndash;63, 2002 ...

{{short description|Family of triangle-free circulant graphs}} ...echt, G. O. Mota, Ch. Reiher, M. Schacht, On the local density problem for graphs of given odd-girth, ''Electronic Notes in Discrete Mathematics'', Volume 62 ...

In [[graph theory]], the '''McKay–Miller–Širáň graphs''' are an infinite class of [[vertex-transitive graph]]s with [[Diameter (g ...l number of vertices can be at most <math>d^2+1</math>. However, only four graphs are known to reach this bound: a single edge (degree one), a 5-vertex [[cyc ...

The individual graphs may be named after the associated solid: ...are isomorphic to the prism graphs, and do not form a separate sequence of graphs. ...

...coloring extension]] on this graph. It is an [[integral graph|integral]] [[Cayley graph]]. It can be represented as a [[Cayley graph]] of the [[abelian group]] <math>Z_n^4</math>.{{r|ks}} ...

...quasirandom group are always bipartite [[pseudorandom graph | quasirandom graphs]]. ...Vera T. Sós | title = Sidon sets in groups and induced subgraphs of Cayley graphs| journal = [[European Journal of Combinatorics]] | volume = 6 | year =1985 ...

...age to a simpler, often convex, space. Hence, obtaining a framework from a Cayley configuration space of a linkage over some set of non-edges is often a matt ...[[Graph flattenability|flattenability]] and [[combinatorial rigidity]] of graphs. ...

...]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Eulerian graph|Eulerian]]<br>[[Cayley graph]] ...endently in 1976<ref>{{citation|first=P. G.|last=Doyle|title=On Transitive Graphs|series=Senior Thesis|publisher=Harvard College|year=1976}}. As cited by Mat ...

An analogue of [[Cayley's theorem]] shows that any semigroup can be realized as a transformation se ==Cayley representation== ...

...]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Integral graph|Integral]]<br>[[Cayley graph]]<br>[[Bipartite graph|Bipartite]] ...COND">[[Marston Conder|Conder, M.]] and Dobcsányi, P. "Trivalent Symmetric Graphs Up to 768 Vertices." J. Combin. Math. Combin. Comput. 40, 41-63, 2002.</ref ...

...gs of Famous Graphs"].</ref><ref>Pegg, E. T. and Exoo, G. "Crossing Number Graphs." Mathematica J. 11, 2009.</ref> ...gons]] of order ''(2,2)'' as proved by Cohen and Tits. They are the split Cayley hexagon ''H(2)'' and its point-line dual. Clearly both of them have the sam ...

==Special classes of graphs== ===Complete graphs=== ...

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

'''''Elementary Number Theory, Group Theory and Ramanujan Graphs''''' is a book in mathematics whose goal is to make the construction of [[R ...y edges connecting it to the remaining parts of the graph. Sparse expander graphs have many important applications in computer science, including the develop ...

...t-free grammar]] for the language <math>\mathcal W(G,X)</math>, that the [[Cayley graph]] <math>\Gamma(G,X)</math> of ''G'' with respect to ''X'' is ''K-tria They then use this triangulability property of the Cayley graph to show that either ''G'' is a finite group, or ''G'' has more than o ...