Let ir(G), γ(G), i(G), β0(G), Γ(G) and IR(G) be the irredundance number, the domination number, the independent domination number, the independence number, the upper domination number and the upper irredundance number of a graph G, respectively. In this paper we show that for any integers k1, k2, k3, k4, k5 there exists a cubic graph G satisfying the following conditions: γ(G)−ir(G) ≥ k1, i(G)−...

A set D of vertices in a graph G is a dominating set if every vertex in V −D is adjacent to some vertex in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A dominating set D of a graph G is total dominating set if the induced subgraph 〈D〉 has no isolated vertices. In this paper, we introduce the total co-independent domination in graphs, exact value for some s...

We establish sharp bounds on the sum and product of the independent domination numbers of a graph and its complement.

Weighted independent domination is an NP-hard graph problem, which remains computationally intractable in many restricted graph classes. In particular, the problem is NP-hard in the classes of sat-graphs and chordal graphs. We strengthen these results by showing that the problem is NP-hard in a proper subclass of the intersection of sat-graphs and chordal graphs. On the other hand, we identify ...