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Spectral conditions for matching extension

Author

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  • Wu, Jiadong
  • Wang, Jing
  • Kang, Liying

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.

Suggested Citation

  • Wu, Jiadong & Wang, Jing & Kang, Liying, 2024. "Spectral conditions for matching extension," Applied Mathematics and Computation, Elsevier, vol. 483(C).
    • Handle: RePEc:eee:apmaco:v:483:y:2024:i:c:s0096300324004430
    DOI: 10.1016/j.amc.2024.128982
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    References listed on IDEAS

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    1. Zhang, Yuke & van Dam, Edwin R., 2023. "Matching extension and distance spectral radius," Other publications TiSEM 4a0d9f56-9439-4b02-a9ec-8, Tilburg University, School of Economics and Management.
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