In a graph \(G = (V(G), E(G))\) , with vertex set V(G) and edge set E(G), a set \(S \subseteq V(G)\) is said to be dominating if every vertex in \(V(G)\setminus S(G)\) has at least one neighbor in S. The domination number of G, denoted by \(\gamma (G)\) , is defined as the minimum cardinality among all dominating sets of V(G). Furthermore, a dominating set S is defined as independent if any two vertices in S are pairwise non-adjacent. The independent domination number of G, denoted by i(G), is the minimum cardinality among all independent dominating sets of G. Determining \(\gamma (G)\) and i(G) for an arbitrary graph are NP-hard problems. In this work, we calculate the domination and independent domination numbers of two subclasses of triangle-free cubic graphs.
