On the incidence Estrada index of graphs (Q2811811)

Let \(A\) and \(D\) be the adjacency matrix and the diagonal matrix of vertex degrees of a graph \(G\). The matrix \(Q=D+A\) is called the signless Laplacian matrix of \(G\) (in analogy to the combinatorial Laplacian matrix \(D-A\)). Let \(\mu_1,\dots,\mu_n\) be the eigenvalues of \(Q\). The authors study the graph invariant \(\sum_{i=1}^n e^{\sqrt{\mu_i}}\), which is named the incidence Estrada index here, and give a few lower and upper bounds for it in terms of the numbers of vertices, edges and \(\sum_{i=1} \sqrt{\mu_i}\).