A Note on the Acquaintance Time of Random Graphs

A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS

The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.

A Note on Strongly Quotient Graphs

The acquaintance time of (percolated) random geometric graphs

In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We focus on G(n, r, p), a random subgraph of a random geometric graph in which n vertices are chosen uniformly at random and independently from [0, 1], and two vertices are adjacent with probability p if the Euclidean distance between them is at most r. We present asymptotic results for the acquaintance time of...

A Tight Upper Bound on Acquaintance Time of Graphs

In this note we confirm a conjecture raised by Benjamini et al. [BST13] on the acquaintance time of graphs, proving that for all graphs G with n vertices it holds that AC(G) = O(n3/2), which is tight up to a multiplicative constant. This is done by proving that for all graphs G with n vertices and maximal degree ∆ it holds that AC(G) ≤ 20∆n. Combining this with the bound AC(G) ≤ O(n2/∆) from [B...

A Note on Tensor Product of Graphs

Let $G$ and $H$ be graphs. The tensor product $Gotimes H$ of $G$ and $H$ has vertex set $V(Gotimes H)=V(G)times V(H)$ and edge set $E(Gotimes H)={(a,b)(c,d)| acin E(G):: and:: bdin E(H)}$. In this paper, some results on this product are obtained by which it is possible to compute the Wiener and Hyper Wiener indices of $K_n otimes G$.