2025/05/20 by Z. H. Zhang, Zhang, Z. H., L. G. Wang +1
Computer Science · Mathematics · #05C50 (Primary) 05C35 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #G.2.2 #Graph Labeling and Dimension Problems #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2505.13863
openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The distance signless Laplacian matrix of a graph G is define as Q(G)=Tr(G)+D(G), where Tr(G) and D(G) are the diagonal matrix of vertex transmissions and the distance matrix of G, respectively. Denote by EG(v) the set of all edges incident to a vertex v in G. A fractional matching of a graph G is a function f:E(G) → [0,1] such that ∑e∈ EG(v) f(e)≤ 1 for every vertex v∈ V(G). The fractional matching number μf(G) of a graph G is the maximum value of ∑e∈ E(G) f(e) over all fractional matchings. Given subgraphs H1, H2,...,Hk of G, a \H1, H2,...,Hk\-factor of G is a spanning subgraph F in which each connected component is isomorphic to one of H1, H2,...,Hk. In this paper, we establish a upper bound for the distance signless Laplacian spectral radius of a graph G of order n to guarantee that μf(G)> (n-k)/(2), where 1≤ k