On the ordering of the Kirchhoff indices of the complements of trees and unicyclic graphs

Abstract

The Kirchhoff index K f (G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the complements of trees and unicyclic graphs. With this method, we determine the first five maximum values of K f ( $$\overline{T}$$ ) and the first four maximum values of K f (Ū), where $$\overline{T}$$ and Ū are the complements of a tree T and unicyclic graph U, respectively.