A subset D of the vertex set V (G) of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D. The minimum cardinality of a dominating set is called the domination number and is denoted by γ(G). A dominating set D such that δ(< D >) = 0 is called an isolate dominating set. The minimum cardinality of an isolate dominating set is called the isolate dominati...

The purpose of this paper is to prove that, with the exception of C 4 , there are no graphs of diameter 2 and maximum degree d with d 2 vertices . On one hand our paper is an extension of [4] where it was proved that there are at most four Moore graphs of diameter 2 (i .e . graphs of diameter 2, maximum degree d, and d2 + 1 vertices) . We also use the eigenvalue method developed in that paper ....

The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...