The Entire Nirmala Index: Theoretical Foundations and Applications

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DOI: https://doi.org/10.28924/2291-8639-24-2026-331
Published: Oct 5, 2026
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Hanaa Alashwali, The Entire Nirmala Index: Theoretical Foundations and Applications, Int. J. Anal. Appl., 24 (2026), 331.

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Hanaa Alashwali

Abstract

In this research work, we introduce a new entire topological index called the entire Nirmala topological index, which is based on the degrees of the graph elements (vertices and edges) along with the adjacency and incidence relations. We establish upper and lower bounds for this new index; exact expressions for some standard families of graphs are obtained, as well as closed formulae for a family of wheel related graphs along with their line graphs. Finally, we present (QSPR) analysis study on the octane isomers, which supports the significance and predictive power of this new index. In both linear and cubic regression models, the new index shows excellent correlation with the properties of the octane isomers. The comparative analysis reflects that the entire Nirmala index is more significant than the Nirmala index. We confirm the excellent predictive power of the entire Nirmala index by a comprehensive residual analysis.

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