Abstract
A graph is called k-extendable if each k-matching can be extended to a perfect matching. We give spectral conditions for the k-extendability of graphs and bipartite graphs using Tutte-type and Hall-type structural characterizations. Concretely, we give a sufficient condition in terms of the spectral radius of the distance matrix for the k-extendability of a graph and completely characterize the corresponding extremal graphs. A similar result is obtained for bipartite graphs.
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