A graph /is said to be G-locally primitive, where G is a subgroup of automorphisms of /-, if the stabiliser G~ of a vertex a acts primitively on the s e t / ( a ) of vertices of / adjacent to or. For a finite non-abelian simple group L and a Cayiey subset S of L, suppose that L <3 G...<Aut( L ) , and the Cayley graph /= Cay ( L, S) is G-locally primitive. In this paper we prove that L is a simp...

In this paper we describe a simple model for random graphs that have an n-fold covering map onto a fixed finite base graph. Roughly, given a base graph G and an integer n, we form a random graph by replacing each vertex of G by a set of n vertices, and joining these sets by random matchings whenever the corresponding vertices are adjacent in G. The resulting graph covers the original graph in t...

There are local operators on (labeled) graphs G with labels (gij) coming from a finite field. If the filed is binary (in other words, if the graph is ordinary), the operations are just the local complementations, but in the general case, there are two different types of operators. The first type is the following: let v be a vertex of the graph and a ∈ Fq, and we obtain a graph with labels g ′ i...

‎the annihilator graph $ag(r)$ of a commutative ring $r$ is a simple undirected graph with the vertex set $z(r)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$‎. ‎in this paper we give the sufficient condition for a graph $ag(r)$ to be complete‎. ‎we characterize rings for which $ag(r)$ is a regular graph‎, ‎we show that $gamma (ag(r))in {1,2}$ and...

In this work we continue the investigation lunched in [4] of the structural properties of the structural properties of the Layers model, a dependent percolation model. Given an undirected graph G = (V,E) and an integer k, let Tk(G) denote the random vertexinduced subgraph of G, generated by ordering V according to Uniform[0, 1] i.i.d. clocks and including in Tk(G) those vertices with at most k ...

We prove that $D_n(3)$, where $ngeq6$ is even, is uniquely determined by its prime graph. Also, if $G$ is a finite group with the same prime graph as $D_4(3)$, then $Gcong D_4(3), B_3(3), C_3(3)$ or $G/O_2(G)cong {rm Aut}({}^2B_2(8))$.

let $g$ be a finite simple graph whose vertices and edges are weighted by two functions. in this paper we shall define and calculate entropy of a dynamical system on weights of the graph $g$, by using the weights of vertices and edges of $g$. we examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. at the end it is shown that, for $rin [0,+infty]$, t...

Let \begin{document}$ \widetilde{X} $\end{document} be a locally finite Gromov hyperbolic graph whose boundary consists of infinitely many points and with cocompact isometric action discrete group \Gamma . We show the uniform Ancona inequality for Brownian motion which implies that \lambda -Martin coincides any \in [0, \lambda_0], in particular at bottom spectrum \lambda_0

Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

An asymmetric coloring of a graph is its vertices that not preserved by any non-identity automorphism the graph. The motion minimal degree group, i.e., minimum number elements are moved (not fixed) automorphism. We confirm Tom Tucker's “Infinite Motion Conjecture” connected locally finite graphs with infinite admit an 2-coloring. infer this from more general result inverse limit sequence permut...