TWO-OUT DEGREE EQUITABLE DOMINATION IN THE MIDDLE, CENTRAL AND THE LINE GRAPHS OF PN, CN AND K1,N

Abstract

Let G=(V,E) be a simple, finite, connected and undirected graph. A dominating set D of G is said to be two-out degree equitable dominating set if for any two vertices u, v ∈ D such that│odD u − odD(v)│ ≤ 2 , where odD u = │N v ∩ (V − D). The minimum cardinality of two -out degree equitable dominating set is called twoout degree equitable domination number and it is denoted by γ2oe(G). In this paper, we introduced the two-out degree equitable domination numbers in the middle, central and the line graphs of the path Pn, cycle Cn and star K1,n graphs.