Independent Semitotal Domination in the Join of Graphs

Abstract

A subset W \(\subseteq\) V (G) of a graph G is an independent semitotal dominating set of G, abbreviated ISTd-set of G, if W is an independent dominating set of G and every element of W is exactly of distance 2 from at least one other element of W. The independent semitotal domination number of G, denoted by \(\gamma\)it2(G), is the minimum cardinality of an ISTd-set of G. In this paper, we study the concept of independent semitotal domination in graphs and investigate the conditions for graphs on which the ISTd-sets exist. Further, the ISTd-sets of the join of any two graphs are examined. Consequently, the corresponding independent semitotal domination number of these graphs are obtained.