The maximum spectral radius of wheel-free graphs

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–Turán type problem: what is the maximum spectral radius of a graph of order n tha...

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Published in:Discrete mathematics 2021-05, Vol.344 (5), p.112341, Article 112341
Main Authors: Zhao, Yanhua, Huang, Xueyi, Lin, Huiqiu
Format: Article
Language:English
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Extremal graph
Quotient matrix
Spectral radius
Wheel-free graph
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description 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–Turán 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–Turán 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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subjects Extremal graph
Quotient matrix
Spectral radius
Wheel-free graph
title The maximum spectral radius of wheel-free graphs
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