Matching, odd [1,b]-factor and distance spectral radius of graphs with given some parameters

2024/01/25 by Zengzhao Xu, Xu, Zengzhao, Weige Xi +2
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2401.14433

openalex publication_date 2024/01/25 · openalex created_date 2024/01/30 · openalex updated_date 2026/07/28

Abstract

For a connected graph G, let μ(G) denote the distance spectral radius of G. A matching in a graph G is a set of disjoint edges of G. The maximum size of a matching in G is called the matching number of G, denoted by α(G). An odd [1, b]-factor of a graph G is a spanning subgraph G₀ such that the degree d_G0(v) of v in G₀ is odd and 1≤ d_G0(v)≤ b for every vertex v∈ V (G). In this paper, we give a sharp upper bound in terms of the distance spectral radius to guarantee α(G)>(n-k)/(2) in an n-vertex t-connected graph G, where 2≤ k ≤ n-2 is an integer. We also present a sharp upper bound in terms of distance spectral radius for the existence of an odd [1,b]-factor in a graph with given minimum degree δ.

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