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Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 8760-8773. doi: 10.3934/mbe.2022406
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On degree–based topological indices of random polyomino chains

  • Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Ave. San Claudio y Río Verde, Col. San Manuel, CU, Puebla 72570, Puebla, Mexico
  • Received: 03 May 2022 Revised: 31 May 2022 Accepted: 07 June 2022 Published: 17 June 2022

  • In this article, we study the degree-based topological indices in a random polyomino chain. The key purpose of this manuscript is to obtain the asymptotic distribution, expected value and variance for the degree-based topological indices in a random polyomino chain by using a martingale approach. Consequently, we compute the degree-based topological indices in a polyomino chain, hence some known results from the existing literature about polyomino chains are obtained as corollaries. Also, in order to apply the results, we obtain the expected value of several degree-based topological indices such as Sombor, Forgotten, Zagreb, atom-bond-connectivity, Randić and geometric-arithmetic index of a random polyomino chain.

    Citation: Saylé C. Sigarreta, Saylí M. Sigarreta, Hugo Cruz-Suárez. On degree–based topological indices of random polyomino chains[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 8760-8773. doi: 10.3934/mbe.2022406

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  • In this article, we study the degree-based topological indices in a random polyomino chain. The key purpose of this manuscript is to obtain the asymptotic distribution, expected value and variance for the degree-based topological indices in a random polyomino chain by using a martingale approach. Consequently, we compute the degree-based topological indices in a polyomino chain, hence some known results from the existing literature about polyomino chains are obtained as corollaries. Also, in order to apply the results, we obtain the expected value of several degree-based topological indices such as Sombor, Forgotten, Zagreb, atom-bond-connectivity, Randić and geometric-arithmetic index of a random polyomino chain.




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