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arXiv · 2406.07821

Walks, infinite series and spectral radius of graphs

Wenqian Zhang
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Abstract

For a graph G, the spectral radius \r{ho}(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we seek the relationship between \r{ho}(G) and the walks of the subgraphs of G. Especially, if G contains a complete multi-partite graph as a spanning subgraph, we give a formula for \r{ho}(G) by using an infinite series on walks of the subgraphs of G. These results are useful for the current popular spectral extremal problem.

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Wenqian Zhang. 2026-08-03. Walks, infinite series and spectral radius of graphs. https://arxiv.org/abs/2406.07821

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