Further results regarding the degree Kirchhoff index of graphs

Abstract

Let G be a connected graph with vertex set V.(G). The degree Kirchhoff index of G is defined as S'(G) = ∑{u,ν} ⊆V.(G) d(u)d(ν)R(u,ν), where d(u) is the degree of vertex u, and R(u,ν) denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result for the degree Kirchhoff index. © 2014 Miskolc University Press.