| Popis: |
Let G = (V, E) be a nontrivial connected graph. A set S ⊂ V is said to be an Exact r-complete dominating set, r≥1 (i) if ∣N(v)∩S∣=1, (ii) ∣N(u)∩(V − S)∣ ≥1 for every ν ∈ V − S, u ∈ S and = m1Kr ∪ m2Kr−1, where m1, m2 are any non negative integers. The cardinality of an minimum exact r-complete dominating is said to be Exact r-complete domination number of G and it is denoted by γer(G). We study the concept of Exact dominating set and generealise this concept and introduce Exact r-complete dominating set in G. The Exact r-complete domination number of several types of graphs are found. In this paper, we investigate some bounds of γer(G) and its relationship with other domination parameters. |
