Spectral conditions for matching extension

Jiadong Wu, Jing Wang and Liying Kang

Applied Mathematics and Computation, 2024, vol. 483, issue C

Abstract: A graph G is called k-extendable if for any matching M of size k in G, there exists a perfect matching of G containing M. Let D(G) and A(G) be the degree diagonal matrix and the adjacency matrix of G, respectively. For 0≤α<1, the spectral radius of Aα(G)=αD(G)+(1−α)A(G) is called the α-spectral radius of G. In this paper, we give a sufficient condition for a graph G to be k-extendable in terms of the α-spectral radius of G and characterize the corresponding extremal graphs. Moreover, we determine the spectral and signless Laplacian spectral radius conditions for a balanced bipartite graph to be k-extendable.

Keywords: α-spectral radius; k-extendable; Extremal graph (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:483:y:2024:i:c:s0096300324004430

DOI: 10.1016/j.amc.2024.128982

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