On the Randi? Index of Quasi-tree Graphs

摘要

The Randi? index of an organic molecule whose molecular graph is 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 vertex u and v in G. A graph G is called quasi-tree, if there exists $uin V(G)$ such that G ? u is a tree. In the paper, we give sharp lower and upper bounds on the Randi? index of quasi-tree graphs.