Zagreb Connection indices on polyomino chains and random polyomino chains

TL;DR

This paper investigates Zagreb connection indices of polyomino chains and their random variants using Markov chain theory, deriving formulas, analyzing extreme values, and exploring long-term behavior.

Contribution

It introduces a Markov chain-based methodology to analyze Zagreb connection indices for both deterministic and random polyomino chains, including formulas and long-term behavior.

Findings

Derived explicit formulas for Zagreb connection indices.

Identified extreme values of the indices.

Analyzed the asymptotic behavior of random polyomino chains.

Abstract

In this manuscript, we delve into the exploration of the first and second Zagreb connection indices of both polyomino chains and random polyomino chains. Our methodology relies on the utilization of Markov chain theory. Within this framework, the article thoroughly examines precise formulas and investigates extreme values. Leveraging the derived formulas, we further explore and elucidate the long-term behavior exhibited by random polyomino chains.