Bounds on the α-Distance Energy and α-Distance Estrada Index of Graphs

Abstract

Let G be a simple undirected connected graph, then DαG=αTrG+1−αDG is called the α-distance matrix of G, where α∈0,1, DG is the distance matrix of G, and TrG is the vertex transmission diagonal matrix of G. In this paper, we study some bounds on the α-distance energy and α-distance Estrada index of G. Furthermore, we establish the relation between α-distance Estrada index and α-distance energy.