Quasi-Laplacian energy of Ψ-sum graphs

As a hot issue in the field of algebraic graph theory, the quasi-Laplacian energy of a graph is a graph invariant in terms of the quasi-Laplacian spectrum, and is versatile in multidisciplinarity, such as social network analysis, theoretical computer science, mathematical chemistry, and so on. Let Gamma be an n-vertex connected graph with quasi Laplacian eigenvalues mu(1) >= mu(2) >= <middle dot> <middle dot> <middle dot> >= mu(n) >= 0. The quasi-Laplacian energy of Gamma is defined as E-Q (Gamma) = Sigma(n)(i=1) mu(2)(i). The psi-sum graphs are generated by utilizing Cartesian product operation for psi (Gamma(1)) and Gamma(2), denoted by Gamma(1+psi) Gamma(2). In this paper, in terms of quasi-Laplacian energy of factor graphs, we characterize the quasi-Laplacian energy of four kinds of psi-sum graphs. As applications, we determine the quasi-Laplacian energy of several special psi-sum graphs generated by base graphs, i.e., path, cycle, complete graph and complete bipartite graph, respectively.