The degree Kirchhoff index of fully loaded unicyclic graphs and cacti

Abstract

Let G be a connected graph with vertex set V(G). The degree Kirchhoff index of G is defined as S'(G) = Σ_(u,V)⊆(G) d(u)d(v)R(u,v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between u and v. In this paper, we characterize n-vertex fully loaded unicyclic graphs having minimum and maximum degree Kirchhoff index. We also determine the extremal cacti with minimum degree Kirchhoff index.