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arXiv · 2204.04650

Maximum principal ratio of the signless Laplacian of graphs

Lele Liu·Shengming Hu·Changxiang He
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Abstract

Let $G$ be a connected graph and $Q(G)$ be the signless Laplacian of $G$. The principal ratio $γ(G)$ of $Q(G)$ is the ratio of the maximum and minimum entries of the Perron vector of $Q(G)$. In this paper, we consider the maximum principal ratio $γ(G)$ among all connected graphs of order $n$, and show that for sufficiently large $n$ the extremal graph is a kite graph obtained by identifying an end vertex of a path to any vertex of a complete graph.

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Lele Liu, Shengming Hu, Changxiang He. 2022-04-10. Maximum principal ratio of the signless Laplacian of graphs. https://arxiv.org/abs/2204.04650

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