Walks, infinite series and spectral radius of graphs

2024/06/12 by Wenqian Zhang, Zhang, Wenqian
Computer Science · Mathematics · Physics and Astronomy · #05C50 #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2406.07821

openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a graph G, the spectral radius \rho(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we seek the relationship between \rho(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 \rho(G) by using an infinite series on walks of the subgraphs of G. These results are useful for the current popular spectral extremal problem.

Related

• Walks and the spectral radius of graphs
• Extremal distance spectral radius of graphs with fixed size
• New bounds on the spectral radius of graphs based on the moment problem
• The spectral radius of graphs without paths and cycles of specified length
• Spectral Radius and Degree Sequence of a Graph