A new upper bound for the Laplacian spectral radius of graphs Original Research Article

Let G = (V, E) be a graph on n vertices. Denote by di = d(vi) the degree of vi set membership, variant V(G). Thenimagewhere image, midNi ∩ Njmid is the number of common neighbors of vi and vj. Moreover, equality holds if and only if G is a bipartite regular graph.