Inverse Domination Numbers to the Kronecker Product of Some Standard Graphs with Path

Abstract

Let G be a non-trivial connected graph with verte???? set V (G). A subset D of V(G) is said to be a dominating set if all the elements of V-D are adjacent with at least one element in D.  A minimum dominating set is a dominating set with minimum cardinality and its value is known as its domination number, denoted by γ (G).

If D′ is a dominating set in V-D is called the inverse dominating set of G with respect to D. The minimum cardinality taken over all inverse dominating sets of G is called the inverse domination number denoted by γ′. In this paper we find the inverse domination number of the resultant graphs obtained by the Kronecker product of some standard graphs with path.