In this paper we present upper bounds on the differences between the independence, domination and irredundance parameters of a graph. For example, using the Brooks theorem on the chromatic number, we show that for any graph G of order n with maximum degree ∆ ≥ 2 IR(G)− β(G) ≤ ⌊ ∆− 2 2∆ n ⌋ , where β(G) and IR(G) are the independence number and the upper irredundance number of a graph G, respect...

Let G = (V,E) be a graph and let v ∈ V. Let IRS(v,G) denote the maximum cardinality of an irredundant set in G which contains v. Then IRS(G) = min {IRS(v,G) : v ∈ V } is called the irredundance saturation number of G. In this paper we initiate a study of this parameter.

In this paper, we survey and supplement the complexity landscape of the domination chain parameters as a whole, including classifications according to approximability and parameterised complexity. Moreover, we provide clear pointers to yet open questions. As this posed the majority of hitherto unsettled problems, we focus on Upper Irredundance and Lower Irredundance that correspond to finding t...

We prove results concerning common neighbours of vertex subsets and irredundance'in the queens graph Qn. We also establish that the lower irredundance number of Q7 is equal to four.