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arXiv · 1709.03407

Asymptotic normality of Laplacian coefficients of graphs

Yi Wang·Haixia Zhang·Baoxuan Zhu
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Abstract

Let $G$ be a simple graph with $n$ vertices and let $$C(G;x)=\sum_{k=0}^n(-1)^{n-k}c(G,k)x^k$$ denote the Laplacian characteristic polynomial of $G$. Then if the size $|E(G)|$ is large compared to the maximum degree $\Delta(G)$, Laplacian coefficients $c(G,k)$ are approximately normally distributed (by central and local limit theorems). We show that Laplacian coefficients of the paths, the cycles, the stars, the wheels and regular graphs of degree $d$ are approximately normally distributed respectively. We also point out that Laplacian coefficients of the complete graphs and the complete bipartite graphs are approximately Poisson distributed respectively.

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Yi Wang, Haixia Zhang, Baoxuan Zhu. 2017-09-11. Asymptotic normality of Laplacian coefficients of graphs. https://arxiv.org/abs/1709.03407

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