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.
From: Wenqian Zhang [view email]
[v1]
Wed, 12 Jun 2024 02:39:55 UTC (10 KB)
[v2]
Fri, 22 Nov 2024 02:55:15 UTC (10 KB)
[v3]
Mon, 26 May 2025 06:23:26 UTC (11 KB)
[v4]
Mon, 3 Aug 2026 15:14:59 UTC (11 KB)
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