<p>A dominating set of a graph provides the fundamental framework for defining domination topological indices. This numerical descriptor combines the concept of domination with graph theory by incorporating vertex domination degrees. In this research work, we introduce the domination elliptic Sombor index&#xa0;(<i>DESO</i>) of a graph. Then, we evaluate the <i>DESO</i> index for several standard graph families as well as for the corona product of two graphs. Additionally, we establish upper and lower bounds for the <i>DESO</i> index in terms of maximum and minimum domination degrees, graph size and various well-known domination topological indices. Moreover, we examine the correlation between the <i>DESO</i> index and other domination topological indices for heptane and octane isomers. The correlation analysis indicates that the domination elliptic Sombor index is strongly correlated with most well-established domination topological indices, highlighting its effectiveness as a new domination degree-based topological index and its potential usefulness in future graph-theoretical applications.</p>