arXiv subjects

U. Vijaya Chandra Kumar

Publications and source records attributed to U. Vijaya Chandra Kumar.

3 recordsLinked to original sources

arXiv2026

A Comparative Study of Exponential Sum-Connectivity and Product-Connectivity Gourava Indices for Benzenoid Hydrocarbons

In this work, the exponential sum-connectivity Gourava index ($e^{SGO(G)}$) and the exponential product-connectivity Gourava index ($e^{PGO(G)}$) are computed and comparatively analyzed for benzenoid hydrocarbons. Our results demonstrate that these descriptors exhibit a strong mutual correlation and provide enhanced sensitivity in modeling the structural characteristics of molecular graphs. Regression analysis reveals that both indices are exceptionally reliable predictors of $π$-electronic energies, achieving correlation coefficients exceeding $0.999$. Notably, a comparative assessment indicates that the exponential product-connectivity variant offers a slightly superior fit, as its coefficients align more precisely with optimal least-squares results. These findings confirm that both exponential Gourava-based indices provide a robust framework for characterizing electronic properties, with the product-connectivity version showing particular promise for high-precision QSPR studies in benzenoid systems.

physics.chem-ph↗

arXiv2025

Edge Irregularity Strength: A Complementary Descriptor to Topological Indices in QSPR and QSAR Studies

In chemical graph theory, topological indices are widely used as numerical descriptors for establishing quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR). These indices successfully correlate molecular structure with various physicochemical and biological properties. In addition to these methods, the concept of edge irregularity strength, a graph labeling measure, offers another perspective for representing structural characteristics. In this context, the edge irregularity strength concept provides a systematic way of assigning numerical labels to atoms based on specific rules. In this work, we explore the chemical applicability of the edge irregularity strength and demonstrate that it can also serve as a predictive tool for physicochemical properties, similar to topological indices. The findings show that the edge irregularity strength captures molecular features and complements existing approaches to structure-property analysis in chemical graph theory.

physics.chem-ph↗

arXiv2025

Vertex energy distributions in regular graph structures

The energy of a vertex $v_i$ in a graph $G$ is defined as $\mathcal{E}_G(v_i) = |A|_{ii}$, where $A$ is the adjacency matrix of $G$, $A^*$ denotes the conjugate transpose of $A$, and $|A| = (AA^*)^{1/2}$. The total energy of the graph, $\mathcal{E}(G)$, is then the sum of the energies of all vertices: $\mathcal{E}(G) = \mathcal{E}_G(v_1) + \mathcal{E}_G(v_2) + \dots + \mathcal{E}_G(v_n)$. In this paper, we compute the vertex energy for several well-known regular graphs, including the Frucht graph, Desargues graph, Tutte-Coxeter graph, Heawood graph, Shrikhande graph, and Petersen graph.

math.CO↗