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arXiv · 2007.06922

The maximum spectral radius of wheel-free graphs

Yanhua Zhao·Xueyi Huang·Huiqiu Lin
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Abstract

A wheel graph is a graph formed by connecting a single vertex to all vertices of a cycle. A graph is called wheel-free if it does not contain any wheel graph as a subgraph. In 2010, Nikiforov proposed a Brualdi-Solheid-Tur\'{a}n type problem: what is the maximum spectral radius of a graph of order $n$ that does not contain subgraphs of particular kind. In this paper, we study the Brualdi-Solheid-Tur\'{a}n type problem for wheel-free graphs, and we determine the maximum (signless Laplacian) spectral radius of a wheel-free graph of order $n$. Furthermore, we characterize the extremal graphs.

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Yanhua Zhao, Xueyi Huang, Huiqiu Lin. 2020-07-14. The maximum spectral radius of wheel-free graphs. https://arxiv.org/abs/2007.06922

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