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Comparative Study of Generalized Sum Graphs via Degree‐Based Topological Indices

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Listed:
  • Muhammad Javaid
  • Saira Javed
  • Ebenezer Bonyah

Abstract

In theoretical chemistry, topological indices (TIs) have important role to predict various physical and structural properties of the study under molecular graphs. Among all topological indices, Zagreb‐type indices have been used more effectively in the chemical literature. In this paper, we have computed first Zagreb, second Zagreb, forgotten, and hyper Zagreb indices of the generalized Q‐sum graph H1QαH2 in the form of different TIs of its basic graphs, where α ≥ 1 is a positive integer. This family of graphs is obtained by the lexicographic product of the graph Qα(H1) and H2, where Qα(H1) is constructed with the help of the generalized line superposition operation Qα on H1. As a conclusion, we also checked the correlation between predefined graph H1[H2] under the operation of lexicographic product H1 and H2 with newly defined generalized Q‐sum graphs H1QαH2 using linear regression models of various degree‐based TIs.

Suggested Citation

  • Muhammad Javaid & Saira Javed & Ebenezer Bonyah, 2022. "Comparative Study of Generalized Sum Graphs via Degree‐Based Topological Indices," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:9001167
    DOI: 10.1155/2022/9001167
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    References listed on IDEAS

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    1. Deng, Hanyuan & Sarala, D. & Ayyaswamy, S.K. & Balachandran, S., 2016. "The Zagreb indices of four operations on graphs," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 422-431.
    2. Zhi-Ba Peng & Saira Javed & Muhammad Javaid & Jia-Bao Liu & Ahmet Sinan Cevik, 2021. "Computing FGZ Index of Sum Graphs under Strong Product," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, March.
    3. Siddiqui, Muhammad Kamran & Imran, Muhammad & Ahmad, Ali, 2016. "On Zagreb indices, Zagreb polynomials of some nanostar dendrimers," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 132-139.
    4. Sarala, D. & Deng, Hanyuan & Ayyaswamy, S.K. & Balachandran, S., 2017. "The Zagreb indices of graphs based on four new operations related to the lexicographic product," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 156-169.
    5. Dalal Awadh Alrowaili & Saira Javed & Muhammad Javaid & Ali Ahmad, 2021. "On the Exact Values of HZ-Index for the Graphs under Operations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-17, November.
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