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This paper characterizes extremal graphs maximizing spectral radius in graphs avoiding fan subgraphs, suggesting inclusion relations across families.
For a graph G, its spectral radius is the largest eigenvalue of its adjacency matrix. A fan H_ is a graph obtained by connecting a single vertex to all vertices of a path of order ≥4. Let SPEX(n,H_) be the set of all extremal graphs G of order n with the maximum spectral radius, where G contains no H_ as a subgraph. In this paper, we completely characterized the graphs in SPEX(n,H_) for any ≥4 and sufficiently large n. An interesting phenomenon was revealed: SPEX(n,H₂ₖ₊₂)⊆ SPEX(n,H₂ₖ₊₃) for any k≥1 and sufficiently large n.
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Wenqian Zhang (2025) studied this question.
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