In this paper, we provide the upper bound on the energy of a graph using the Diaz-metcalf inequality. Then, we obtained several bounds on the energy of a graph with given invariants such as order, size, diameter, radius, girth, kirchoff index, clique number, algebraic connectivity, vertex connectivity, index, etc. Finally, we obtain several bounds on the energy of a graph in terms of many topological indices such as harmonic index, symmetric division degree index and modified second Zagreb indices.
Topological indices are numerical descriptors used in chemical graph theory to characterize the size, branching and connectivity of molecular structures. These descriptors are significantly correlated with a range of physicochemical characteristics and biological activities of a molecular compound. Recently, the M-polynomial approach has been used to represent molecular structures and calculate degree-based topological indices for various graph structures. This study focuses on determining closed-form expressions of the M-polynomial for three types of silicon-carbon structures: SiC3-I[a,b], SiC3-II[a,b] and SiC3-III[a,b], for arbitrary a>1, b≥1. Using the obtained M-polynomial, we calculate nine degree-dependent indices for these silicon-carbide structures. The study also includes visualizations of the computed topological indices and the M-polynomial. Furthermore, we have done a novel comparative analysis among the topological indices for these specific structures. The results obtained in this study provide a mathematical foundation for future researchers in the property prediction of these structures.
Shibsankar Das, Shahzadi Nargis· Scientific Annals of Compute...· 0 citations
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