Matching extension and distance spectral radius

• DOI: 10.1016/j.laa.2023.06.002
• Publication Date: 2023-06-03T00:52:14Z
• Authors: Yuke Zhang; Edwin R. van Dam
• Keywords: Spectral Radius

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.