Bounds on the $α$-distance spectrum of graphs

Abstract

For a simple, undirected and connected graphis the distance matrix of G, and T r(G) is the vertex transmission diagonal matrix of G. Recently, the α-distance energy of G was defined based on the spectra of D α (G). In this paper, we define the α-distance Estrada index of G in terms of the eigenvalues of D α (G). And we give some bounds on the spectral radius of D α (G), α-distance energy and α-distance Estrada index of G.