On the Incidence Energy of Some Toroidal Lattices

Abstract

The incidence energy $\text{I}\text{E}(G)$, defined as the sum of the singular values of the incidence matrix of $G$, is a much studied quantity with well known applications in chemical physics. In this paper, we derived the closed-form formulae expressing the incidence energy of the 3.12.12 lattice, triangular kagomé lattice, and $S(m,n)$ lattice, respectively. Simultaneously, the explicit asymptotic values of the incidence energy in these lattices are obtained by utilizing the applications of analysis method with the help of software calculation.