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Bounds on the Neighborhood Inverse Sum In-degree Index of Graphs with Applications to Benzenoid | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 آذر 1404 اصل مقاله (1.19 M) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30619.2555 | ||
| نویسندگان | ||
| Deepa Balasubramaniyan1؛ Natarajan Chidambaram1؛ Modjtaba Ghorbani* 2 | ||
| 1Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam - 612 001, Tamil Nadu, India | ||
| 2Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-163, Iran | ||
| چکیده | ||
| The neighborhood inverse sum indeg index, denoted as $ISI_N(\mathcal{G})$, of a simple graph $\mathcal{G}$ is defined as the sum of the terms $( \frac{\mathscr{\delta}_{\mathcal{G}}(\mathscr{r})\mathscr{\delta}_{\mathcal{G}}(\mathscr{s})}{\mathscr{\delta}_{\mathcal{G}}(\mathscr{r})+\mathscr{\delta}_{\mathcal{G}}(\mathscr{s})} \) for all edges \( \mathscr{\mathscr{rs}} )$ in $\mathcal{G}$. Here, \( \mathscr{\delta}_{\mathcal{G}}(\mathscr{r}) \) represents the neighborhood degree of a vertex \( \mathscr{r} \), which is the sum of the degrees of the neighbours of \( \mathscr{r} \) in \( \mathcal{G} \). This article establishes bounds for the \( ISI_N(\mathcal{G}) \) index in relation to various graph invariants and its connection to neighborhood degree-sum-based topological indices. We also present results on the \( ISI_N \) index concerning different graph operations. Furthermore, we analyze the physico-chemical properties of 55 benzenoid hydrocarbons and validate our model with 10 more benzenoid hydrocarbons. | ||
| کلیدواژهها | ||
| Inverse Sum In-degree Index؛ vertex degree؛ Benzenoid Hydrocarbons | ||
| مراجع | ||
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