On Bond Incident Degree Indices of Random Spiro Chains

Abstract

Let $G=(V(G),E(G))$ denote a graph, many important topological indices can be defined as $TI(G)=\sum _{vu\in E(G)}f(d_v,d_u).$ In this paper, we study these kinds of topological indices in random spiro chains via a martingale approach. In which their explicit analytical expressions of the exact distribution, expected value, and variance are obtained. As n goes to $\infty ,$ the asymptotic normality of topological indices of a random spiro chain is established through the Martingale Central Limit Theorem. In particular, we compute the Nirmala, Sombor, Randić, and Zagreb index for a random spiro chain along with their comparative analysis.

Keywords:

• Sombor index
• random chains
• martingales
• Randić index
• Zagreb index

Acknowledgments

All three authors would like to thank three anonymous referees for valuable comments that definitely help improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data generated or analyzed during this study are included in this published article.