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.

中文翻译：

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无轮图的最大光谱半径

轮图是通过将单个顶点连接到循环的所有顶点而形成的图。如果图不包含任何轮图作为子图，则称为无轮图。在2010年，Nikiforov提出了Brualdi–Solheid–Turán类型的问题：有序图的最大光谱半径是多少$ñ$不包含特定种类的子图。在本文中，我们研究了无轮图的Brualdi–Solheid–Turán型问题，并确定了无序图的最大（无符号拉普拉斯算子）谱半径$ñ$。此外，我们刻画了极值图。