a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

In this paper we investigate the Green‎ ‎graphs for the regular and inverse semigroups by considering the‎ ‎Green classes of them‎. ‎And by using the properties of these‎ ‎semigroups‎, ‎we prove that all of the five Green graphs for the‎ ‎inverse semigroups are isomorphic complete graphs‎, ‎while this‎ ‎doesn't hold for the regular semigroups‎. ‎In other words‎, ‎we prove‎ ‎that in a regular se...

in this paper we investigate the green‎ ‎graphs for the regular and inverse semigroups by considering the‎ ‎green classes of them‎. ‎and by using the properties of these‎ ‎semigroups‎, ‎we prove that all of the five green graphs for the‎ ‎inverse semigroups are isomorphic complete graphs‎, ‎while this‎ ‎doesn't hold for the regular semigroups‎. ‎in other words‎, ‎we prove‎ ‎that in a regular se...

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...

In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of S+(U) and S+(U2) for regular graphs and show that S+(U2) = S+(U)2 + I.