New Bounds for the Generalized Distance Spectral Radius/Energy of Graphs

摘要

Let G be a simple connected graph with vertex set VG=v1,v2,…,vn and dvi be the degree of the vertex vi. Let DG be the distance matrix and TrG be the diagonal matrix of the vertex transmissions of G. The generalized distance matrix of G is defined as DαG=αTrG+1?αDG, where 0≤α≤1. If λ1,λ2,…,λn are the eigenvalues of DαG, then the generalized distance spectral radius of G is defined as ρDαG=max1≤i≤nλi. The generalized distance energy of G is EDαG=∑i=1nλi?2αWG/n, where WG is the Wiener index of G. In this paper, we give some bounds of the generalized distance spectral radius and the generalized distance energy.