The first six quasi-trees with greatest randić index

Abstract

The connectivity index (the Randić index) of a graph G is the sum of the weights (d(u)d(v))^-1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. A graph G is called quasi-tree, if there exists v ε V(G) such that G - v is a tree. In this paper, we will give the first six quasi-trees with greatest Randić index.