This work introduces two greedy heuristic approaches specifically designed for the dominating tree problem (DTP). Given a connected graph \(G = (V, E)\) with positive costs associated with its edges, the DTP seeks a tree \(T \subseteq G\) , such that each node \(v \in V\) is either part of T or directly connected to a node in T, and that minimizes the sumtotal of its edge-costs. It is an \(\mathcal{N}\mathcal{P}\) -hard combinatorial optimization problem and appears in several practical applications, especially those pertaining to wireless sensor networks. Effectiveness of the presented heuristics has been assessed by comparing them with previous problem-specific heuristic approaches on the test instances available in the literature. Computational results clearly demonstrate the superiority of the presented heuristics in comparison to previous problem-specific heuristic approaches.