Equality of Domination and Inverse Domination Numbers

T. Tamizh Chelvam Department of Mathematics Manonmaniam Sundaranar University Tirunelveli 627 012 Tamil Nadu, India Email: tamche_59@yahoo.co.in G. S. Grace Prema Department of Mathematics St. John’s College Tirunelveli – 627 002 Tamil Nadu, India. Abstract: A set D of vertices of a graph G is a dominating set if every vertex of V-D is adjacent to at least one vertex in D. The domination number ) (G γ is the minimum cardinality of a dominating set of G. A subset of V-D, which is also a dominating set of G is called the inverse dominating set of G with respect to D. The inverse domination number of G, ) (G γ ′ is the minimum cardinality of the inverse dominating sets. In this paper, some graphs with equal domination and inverse domination numbers are identified.