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 using Tutte-type Hall-type structural characterizations. Concretely, we sufficient condition in terms radius distance matrix completely characterize corresponding extremal graphs. similar result obtained

Let G be an undirected 2-edge connected graph with nonnegative edge weights and a distinguished vertex z. For every node consider a shortest cycle containing this node and z in G. The cycle-radius of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle-radius of H is similarly defined except that cycles are replaced by directe...