Inequalities relating domination parameters in cubic graphs Original Research Article

The following sequence of inequalities is well-known in domination theory: ir ⩽ γ ⩽ i ⩽ β0 ⩽ ⌈ ⩽ IR. In this chain, ir and IR are the irredundance and upper irredundance numbers, respectively, γ and ⌈ are the domination and upper domination numbers, and i and β0 are the independent domination and vertex independence numbers. In this paper we investigate the above chain of inequalities for cubic graphs, i.e., regular graphs of degree 3. We attempt to extend the above chain for cubic graphs by including the parameters γ−, ⌈−, γs and ⌈s, where γ− and ⌈ are the minus domination and upper minus domination numbers, respectively, and γs and ⌈s are the signed domination and upper signed domination numbers, respectively.