Fractional matching number and spectral radius of nonnegative matrices of graphs

A fractional matching of a graph G is a function f:E(G) → [0, 1] such that for any v ∈ V(G), where E G (v) = {e ∈ E(G): e is incident with v in G}. The fractional matching number of G is is a fractional matching of G}. For any real numbers a ≥ 0 and k ∈ (0, n), it is observed that if n = |V(G)| and...

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Bibliographic Details
Published in:Linear & multilinear algebra 2022-12, Vol.70 (19), p.4133-4145
Main Authors: Liu, Ruifang, Lai, Hong-Jian, Guo, Litao, Xue, Jie
Format: Article
Language:English
Subjects:
fractional matching
fractional perfect matching
Nonnegative matrix
quotient matrix
spectral radius
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Summary:A fractional matching of a graph G is a function f:E(G) → [0, 1] such that for any v ∈ V(G), where E G (v) = {e ∈ E(G): e is incident with v in G}. The fractional matching number of G is is a fractional matching of G}. For any real numbers a ≥ 0 and k ∈ (0, n), it is observed that if n = |V(G)| and , then . We determine a function φ(a, n, δ, k) and show that for a connected graph G with n = |V(G)|, , spectral radius λ 1 (G) and complement , each of the following holds. If λ 1 (aD(G) + A(G)) 
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2020.1865252