Graphs with maximum Laplacian and signless Laplacian Estrada index

The Laplacian Estrada index (LEELEE) and the signless Laplacian Estrada index (SLEESLEE) of a graph GG are, respectively, the sum of the exponentials of the eigenvalues of the Laplacian and signless Laplacian matrix of GG. The vertex frustration index υbυb of a graph GG is the minimum number of vertices whose deletion from GG results in a bipartite graph. Graphs having maximum LEELEE and SLEESLEE values are determined among graphs with nn vertices and 1≤υb≤n−31≤υb≤n−3.