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.
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