A NOTE ON SOME LOWER BOUNDS OF THE LAPLACIAN ENERGY OF A GRAPH.

For a simple connected graph G of order n and size m, the Laplacian energy of G is defined as LE(G) = where µ1,µ2,..., µn-1; µn are the Laplacian eigenvalues of G satisfying µ1 ≥ µ2 ≥ ... ≥ µn-1 > µn = 0. In this note, some new lower bounds on the graph invariant LE(G) are derived. The obtained results are compared with some already known lower bounds of LE(G). [ABSTRACT FROM AUTHOR]