Sharp Bounds for Spectral Radius of Graphs Presented by K-Neighbour of the Vertices

Abstract

Let G = (V, E) be a simple connected graph with V (G) = {v1, v2, …, vn} and degree sequence d1, d2, …, dn. Denote , where k is a positive integer number and vi∈V(G) and note that t0(i)=di. Let ρ(G) be the largest eigenvalue of adjacent matrix of G. In this paper, we present sharp upper and lower bounds of ρ(G) in terms of mk(i) (see theorem (2.1)). From which, we can obtain some known results, and our result is better than other results in some case.