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Research Paper | Mathematics | Volume 15 Issue 3, March 2026 | Pages: 1919 - 1925 | India
Augmented Euler Sombor Indices on Lexicographic Product of Open Neighborhood Graphs
Abstract: This paper introduces and investigates the Augmented Euler Sombor (AES) index and the Reciprocal Augmented Euler Sombor (RAES) index in the context of lexicographic product graphs formed from open neighborhood graphs. By merging the structural richness of Euler Sombor-type degree-based topological indices with the hierarchical complexity of lexicographic products over open neighborhood graphs, we derive exact closed-form formulas for eight novel theorems covering cycle, complete, and complete bipartite graph families and their open neighborhood counterparts. Each theorem is supported by detailed proofs and computational examples verified via MATLAB. We also apply the AES index to three prominent chemical drug structures- chloroquine, hydroxychloroquine, and remdesivir revealing quantitative correlations between molecular topology and index values. Comparative analysis with classical Sombor, Euler Sombor, and related indices demonstrates that the AES framework offers superior structural sensitivity. Our findings establish a foundational methodology bridging discrete graph theory, chemical graph theory, and network science.
Keywords: Augmented Euler Sombor index, Open neighborhood graph, Lexicographic product, Topological indices, Chemical graph theory
How to Cite?: Dr. Akkilli Naresh, Rudrapati Bhuvaneswara Prasad, "Augmented Euler Sombor Indices on Lexicographic Product of Open Neighborhood Graphs", Volume 15 Issue 3, March 2026, International Journal of Science and Research (IJSR), Pages: 1919-1925, https://www.ijsr.net/getabstract.php?paperid=SR26329142158, DOI: https://dx.dx.doi.org/10.21275/SR26329142158