An always nontrivial upper bound for Laplacian graph eigenvalues Original Research Article

Let G be a graph on vertex set image Let di be the degree of vi, let Ni be the set of neighbours of vi and let S be the number of vertices of Ssubset of or equal toV. In this note, we prove thatimageis an upper bound for the largest eigenvalue of the Laplacian matrix of G. For any G, this bound does not exceed the order of G.