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arXiv · 1503.07841

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

Jia-Bao Liua·Xiang-Feng Pan
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Abstract

The incidence energy $\mathscr{IE}(G)$ 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.

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Jia-Bao Liua, Xiang-Feng Pan. 2015-03-18. Asymptotic incidence energy and Laplacian-energy-like invariant of the Union Jack lattice. https://arxiv.org/abs/1503.07841

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