Some new results on captive dominating sets in graphs.

A dominating set D ⊂ V (G) is said to be a captive dominating set of G if 〈 D 〉 has no isolated vertex (D is a total dominating set) and each vertex v ∈ D is adjacent to at least one vertex in V − D. A captive dominating set D is said to be a minimal captive dominating set if no proper subset D ′ of D is a captive dominating set. The minimum cardinality of a minimal captive dominating set of G is called the captive domination number of G which is denoted by γ c a (G). In this paper, we have characterized some results, determine the values of the domination-related parameters for the graph and its splitting graph, relate captive domination and packing number of a graph, etc. We have also constructed graphs for which γ c a > γ t. [ABSTRACT FROM AUTHOR]