A new upper bound for the Laplacian spectral radius of a graph

Abstract

Let G be a simple connected graph with m edges, and the line graph of G with degree sequence t1 ≥ t2 ≥ · · · ≥ tn. This paper presents a new upper bound for the Laplacian spectral radius of G as follows:
µ1(G) ≤ min 1≤i≤m{(ti + 3 +p(ti + 1)2 + 4(i − 1)(t1 − ti) /2)}.