The bondage number of the strong product of a complete graph with a path and a special starlike tree

Abstract

The bondage number [Formula: see text] of a graph [Formula: see text] is the cardinality of a minimum edge set whose removal from [Formula: see text] results in a graph with the domination number greater than that of [Formula: see text]. It is a parameter to measure the vulnerability of a communication network under link failure. In this paper, we obtain the exact value of the bondage number of the strong product of a complete graph and a path. That is, for any two integers [Formula: see text] and [Formula: see text], [Formula: see text] if [Formula: see text]; [Formula: see text] if [Formula: see text] (mod 3); [Formula: see text] if [Formula: see text] (mod 3). Furthermore, we determine the exact value of the bondage number of the strong product of a complete graph and a special starlike tree.