Abstract

The Laplacian-energy-like invariant, LEL, is the sum of the square roots of the Laplacian eigenvalues of the underlying graph G. The incidence energy IE is the sum of the square roots of the signless Laplacian eigenvalues of G. The vertex bipartiteness v(b) of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. Graphs having maximum LEL and IE values are determined among graphs with a fixed number n of vertices and fixed vertex bipartiteness, 1 <= v(b) <= n - 3.