The maximum spectral radius of wheel-free graphs
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\'an 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\'an 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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