Upper bounds on the Laplacian energy of some graphs

作者：Robbiano Maria^*; Martins Enide Andrade; Jimenez Raul; San Martin Bernardo

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2010, 64(1): 97-110.

The Laplacian energy LE[G] of a simple graph G with n vertices and m edges is equal to the sum of distances of the Laplacian eigenvalues to their average. For 1 <= j <= s, let A(j) be matrices of orders n(j). Suppose that
det(L(G) - lambda I(n)) = Pi(s)(j=1) det(A(j) - lambda I(nj))(tj),
with tj > 0. In the present paper we prove
LE[G] <= Sigma(s)(j=1) tj root nj parallel to Aj - 2m/n I(nj) parallel to (F) <= root n parallel to L (G) - 2m/m I(n) parallel to (F), where parallel to center dot parallel to (F,)
stands for the Frobenius matrix norm.

• 出版日期2010