Bounds on the Neighborhood Inverse Sum In-degree Index of Graphs with Applications to Benzenoid

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam - 612 001, Tamil Nadu, India

2 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-163, Iran

Abstract

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.

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References

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Communications in Combinatorics and Optimization

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