A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph Original Research Article

Let G be a simple connected graph with n vertices. The largest eigenvalue of the Laplacian matrix of G is denoted by μ(G). Suppose the degree sequence of G is d1greater-or-equal, slantedd2greater-or-equal, slantedcdots, three dots, centeredgreater-or-equal, slanteddn. In this paper, we present a sharp upper bound of μ(G) image the equality holds if and only if G is a regular bipartite graph