International Journal of Mathematics And Computer Research

Abstract

Let G= (V,E) be a simple graph. A subset D of V(G) is said to be a dominating set of G if for every vertex vV-D there exists a vertex uD such that u and v are adjacent in G. A subset D of V(G) is called a complementary degree equitable dominating set (cdged-set) of G if D is a dominating set of G and V-D is a degree equitable set in G. The minimum cardinality of a minimal cdged-set of G is called the complementary degree equitable domination number of G and is denoted by cdged (G). The maximum cardinality of a minimal cdged-set of G is called the upper complementary degree equitable domination number of G and is denoted by cdged(G). Complementary degree equitable domination is super hereditary. Therefore, complementary degree equitable domination is minimal if and only if it is 1-minimal. Interesting results are proved with respect to the new parameters.