On k-restricted connectivity of direct product of graphs.

Let G be a graph. A vertex-cut S of G is said to be k-restricted if every component of G − S has at least k vertices, and cyclic if G − S has at least two components which contain a cycle. The minimum cardinality over all k -restricted vertex-cuts of G is called the k-restricted connectivity of G and is denoted by κ k (G). Also the minimum cardinality over all cyclic vertex-cuts of G is called the cyclic connectivity of graph G and is denoted by κ c (G). In this paper, the k -restricted connectivity and cyclic connectivity of the direct product of two graphs G 1 and G 2 is obtained for some k ≥ 2 , where G 1 is a complete graph, and G 2 is a complete graph, a complete bipartite graph or a cycle. [ABSTRACT FROM AUTHOR]