Variations on domination in graphs containing edge-disjoint cycles

Abstract

The concept of domination in graphs, with its many variations, is now well studied in graph theory. In this paper, we focus on independent sets and two variations on domination theme that are well studied in graph theory called total domination and restrained domination. A sub set is an independent set, if no two vertices of S are adjacent. A subset  is called a dominating set, if every vertices of V-S is adjacent to a member of S. We will consider independent sets and variant dominating sets in the graphs contain edge-disjoint cycles.