Graphs with maximum Laplacian and signless Laplacian Estrada index

Abstract

The Laplacian Estrada index (LEE) and the signless Laplacian Estrada index (SLEE) of a graph G are, respectively, the sum of the exponentials of the eigenvalues of the Laplacian and signless Laplacian matrix of G. The vertex frustration index υb of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. Graphs having maximum LEE and SLEE values are determined among graphs with n vertices and 1≤υb≤n−3.