A New Upper Bound for Laplacian Graph Eigenvalues

摘要

Let G = (V,E) be a graph with vertex set V = {v_1 , v_2,n}.The degree of v_iand the average theadjacent vertices of v_iare denoted byd_iand m_(vi), respectively. In this paper, we prove that max{d_vm_v/u+um_/d_v:uvE}is anupper bound for the largest Laplacian eigenvalue of G, the equality holds if G is a d-regular bipartite graph.