<p>This study introduces a new class of closed neighborhood degree-based topological descriptors. To provide a unified approach for their analysis, we introduce CM-polynomial, which encodes closed neighborhood degree information and facilitates the systematic derivation of newly formulated indices using operator-based calculus. The effectiveness of these descriptors is demonstrated on octane isomers by computing closed neighborhood degree-based measures and examining their correlations with six key physico-chemical properties. These findings highlight their strong predictive capability in QSPR/QSAR studies. Additionally, the CM-polynomial demonstrates enhanced isomer discrimination capability, as evidenced by its high sensitivity values compared to M-polynomial. The CM-polynomial proves to be a versatile framework in chemical graph theory and an effective tool for modeling molecular properties. Further, explicit formulas for CM-polynomial are established for several standard classes of graphs.</p>