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- Title
Fractional Matchings in Graphs from the Spectral Radius.
- Authors
Chen, Qian-Qian; Guo, Ji-Ming; Wang, Zhiwen
- Abstract
Denote by G n , ν ∗ (G n , ν ∗ ∗) the collection of all (connected) graphs of order n having a fractional matching number ν ∗ . This paper characterizes the graphs in G n , ν ∗ and G n , ν ∗ ∗ with the maximum spectral radius, and establishes a lower bound for the spectral radius of graphs of order n to guarantee that their fractional matching numbers are at least τ + 1 2 . In addition, we explore the relationship between the spectral radius, perfect matching and fractional perfect matching of G. Moreover, we present a spectral condition guaranteeing that the matching number of a graph is at least k + 1 , which generalizes some previous known results.
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2024, Vol 47, Issue 4, p1
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-024-01706-3