Two Complemented Edge Isolated Domination of a Cycle Graph Dr. Sumathi P.*, Felicia R. Esther** *C. Kandaswami Naidu College for Men, Chennai, India **Shri Krishnaswamy College For Women, Chennai, India Online published on 14 October, 2016. Abstract Let G = (V, E) be a non trivial, finite graph with vertex set V and edge set E. A subset S of V in a graph G is said to be an edge-dominating set if every edges in G is adjacent to a vertex in S. A edge dominating set S such that S has an isolated vertex or V−S is a single vertex is called edge isolated dominating set. The minimum cardinality of edge isolated dominating set is called edge isolated domination number of G and it is denoted by γei(G). Two complement of a graph G is obtained by partitioning its V(G) into two subsets V1 and V2 such that every edge (a, b) ∈ G is either belongs to V1 or V2 only if a, b ∈ V1 or V2, and there exist a new edge (c, d) between every vertices of V1 and its non-adjacency vertices in G which are in V2. Two complement of a graph G is denoted by G2p. The edge isolated dominating set of a two complemented graph is called the two complemented edge isolated dominating set. The minimum cardinality of two complemented edge isolated dominating set is called two complemented edge isolated domination number of G and it is denoted by γei(G2p). In this paper the exact value of γei(G2p) is calculated for cycle graph. Top Keywords Edge dominating set, Edge isolated dominating set, Edge isolated domination number, Two complemented edge isolated dominating set, two complemented edge isolated domination number. Top |