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Bibliographic Details
Main Author: Zhang, Wenqian
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.07821
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author Zhang, Wenqian
author_facet Zhang, Wenqian
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_07821
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Walks, infinite series and spectral radius of graphs
Zhang, Wenqian
Combinatorics
05C50
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.
title Walks, infinite series and spectral radius of graphs
topic Combinatorics
05C50
url https://arxiv.org/abs/2406.07821