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arXiv · 2204.07798

The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs

Tingzeng Wu·Tian Zhou
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Abstract

Let $G$ be a graph with $n$ vertices, and let $L(G)$ and $Q(G)$ be the Laplacian matrix and signless Laplacian matrix of $G$, respectively. The polynomial $π(L(G);x)={\rm per}(xI-L(G))$ (resp. $π(Q(G);x)={\rm per}(xI-Q(G))$) is called {\em Laplacian permanental polynomial} (resp. {\em signless Laplacian permanental polynomial}) of $G$. In this paper, we show that two classes of bicyclic graphs are determined by their (signless) Laplacian permanental polynomials.

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Tingzeng Wu, Tian Zhou. 2022-04-16. The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs. https://arxiv.org/abs/2204.07798

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