The Domination Reciprocal Mean Square Index

Abstract: We introduce the Domination Reciprocal Mean Square index (DRMS), a new domination-degree-based topological index obtained by replacing the ordinary degree in the reciprocal mean square index with the domination degree. We establish elementary bounds in terms of graph size and extremal domination degrees, derive a one-parameter family of sharp lower bounds via the power mean, and obtain sharp bounds in terms of several well-known domination-degree-based indices, with a full characterization of the equality cases. We also compute closed-form expressions for (DRMS) on several standard graph families and for the corona product of two graphs.