The degree resistance distance of cacti

Abstract

© 2015 Elsevier B.V. All rights reserved. Graph invariants, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph G is defined as DR(G) = Σ{u, v}⊆V(G)[d(u) + d(v)]R(u, v), where d(u) is the degree of the vertex u, and R(u, v) the resistance distance between the vertices u and v. Let Cact(n; t) be the set of all cacti possessing n vertices and t cycles. The elements of Cact(n; t) with minimum degree resistance distance are characterized.