k-Domination Connectivity in Graphs

The conditional connectivity of [Formula: see text] with respect to a graph theoretic property [Formula: see text] is the smallest cardinality of a set [Formula: see text] of vertices (edges), if any, such that every component [Formula: see text] of the disconnected graph [Formula: see text] has property [Formula: see text]. Connectivity and domination are two major areas of graph theory having numerous applications in computer and information sciences. In this paper, we study a type of conditional connectivity that combines connectivity and domination, called [Formula: see text]-domination connectivity. Further, we investigate the [Formula: see text]-domination connectivity of some standard graph classes.