Asymptotic incidence energy and Laplacian-energy-like invariant of the Union Jack lattice

The incidence energy I E (G) of a graph G, defined as the sum of the singular values of the incidence matrix of a graph G, is a much studied quantity with well known applications in chemical physics. The Laplacian-energy-like invariant of G is defined as the sum of square roots of the Laplacian eigenvalues. In this paper, we obtain the closed-form formulae expressing the incidence energy and the Laplacian-energy-like invariant of the Union Jack lattice. Moreover, the explicit asymptotic values of these quantities are calculated by utilizing the applications of analysis approach with the help of calculational software.