Total and Inverse Domination Numbers of Certain Graphs

Abstract

For any graph G having vertex set V(G) then the subset set D ⊆ V(G) is known as a dominating set if every single vertex of G not belonging to D is adjoining to not less than one vertex in D. The domination number γ(G) is the minimum number of elements contained in a minimum dominating set D of G. Any subset D in V(G) is known as total domianting set if each and every vertex of V in G is adjoining to not less than one vertex of D. The set which contains minimum number of elements among all total dominating set is the minimum total dominating set and its cardinality denoted as total domination number γ t ( G). The inverse dominating set D ′ is defined as that D is a minimum dominating set of G, if there exist an another dominating set say D ′ in V − D corresponding to D and its cardinality is the inverse domination number γ ′(G). In this paper we give the total and inverse domination numbers of certain graphs.