Abstract: A set X is independent if no two vertices of X are adjacent. A set X is dominating if N[X]=V(G). A dominating set X is minimal if no set X\{x} with x∈ X
is dominating. The independence number i(G)(\beta(G)) is the minimum (maximum) cardinality of a maximal independent set of G. The domination number γ(G) (the upper domination number Γ(G)) is the minimum (maximum) cardinality of a minimal dominating set of G. In this paper, we prove that: (1) if G ∈ R and G is a cubic graph of order n, then γ(G)=i(G), β(G)=n/3; (2) for every connected claw-free cubic graph G of order n, if G(G≠ K₄) contains no K₄-e as induced subgraph, then β(G)=n/3.

Key words: Cubic graph, The domination number, The independence number, Colouring.