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arXiv · 1406.7501

Asymptotic Laplacian-Energy-Like Invariant of Lattices

Jia-Bao Liu·Xiang-Feng Pan·Fu-Tao Hu·Feng-Feng Hu
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Abstract

Let $μ_1\ge μ_2\ge\cdots\geμ_n$ denote the Laplacian eigenvalues of $G$ with $n$ vertices. The Laplacian-energy-like invariant, denoted by $LEL(G)= \sum_{i=1}^{n-1}\sqrt{μ_i}$, is a novel topological index. In this paper, we show that the Laplacian-energy-like per vertex of various lattices is independent of the toroidal, cylindrical, and free boundary conditions. Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in these lattices are obtained. Moreover, our approach implies that in general the Laplacian-energy-like per vertex of other lattices is independent of the boundary conditions.

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Jia-Bao Liu, Xiang-Feng Pan, Fu-Tao Hu, Feng-Feng Hu. 2014-06-29. Asymptotic Laplacian-Energy-Like Invariant of Lattices. https://arxiv.org/abs/1406.7501

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