Liu, Wu-xin; Wei, Fu-yi On the incidence Estrada index of graphs. (English) Zbl 1344.05091 Util. Math. 98, 43-52 (2015). 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 \(\sum_{i=1} \sqrt{\mu_i}\). Reviewer: Dragan Stevanović (Niš) MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C07 Vertex degrees 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) Keywords:signless Laplacian matrix; incidence energy; Estrada index; Nordhaus-Gaddum inequality PDFBibTeX XMLCite \textit{W.-x. Liu} and \textit{F.-y. Wei}, Util. Math. 98, 43--52 (2015; Zbl 1344.05091)