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First zagreb spectral radius of unicyclic graphs and trees

Author

Listed:
  • Parikshit Das

    (National Institute of Technology Durgapur)

  • Kinkar Chandra Das

    (Sungkyunkwan University)

  • Sourav Mondal

    (Sungkyunkwan University
    SRM Institute of Science and Technology)

  • Anita Pal

    (National Institute of Technology Durgapur)

Abstract

In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are $$d_{u_i}+d_{u_j}$$ d u i + d u j , if $$u_i$$ u i is connected to $$u_j$$ u j ; 0, otherwise, where $$d_{u_i}$$ d u i is degree of i-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius ( $$\rho _1$$ ρ 1 ) associated with this matrix. The lower and upper bounds of $$\rho _1$$ ρ 1 are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of $$\rho _1$$ ρ 1 is also explained.

Suggested Citation

  • Parikshit Das & Kinkar Chandra Das & Sourav Mondal & Anita Pal, 2024. "First zagreb spectral radius of unicyclic graphs and trees," Journal of Combinatorial Optimization, Springer, vol. 48(1), pages 1-24, August.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:1:d:10.1007_s10878-024-01195-x
    DOI: 10.1007/s10878-024-01195-x
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    References listed on IDEAS

    as
    1. Huan He & Miaolin Ye & Huan Xu & Guidong Yu, 2023. "RETRACTED ARTICLE: On $${A_{\alpha }}$$ A α -spectrum of a unicyclic graph," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-16, January.
    2. Seyed Mahmoud Sheikholeslami & Akbar Jahanbani & Rana Khoeilar, 2021. "New Results on Zagreb Energy of Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, May.
    3. Bo Deng & Caibing Chang & Kinkar Chandra Das, 2023. "RETRACTED ARTICLE: The Sachs theorem and its application on extended adjacency matrix of graphs," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-12, January.
    4. Roberto Cruz & Juan Daniel Monsalve & Juan Rada, 2021. "The balanced double star has maximum exponential second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 544-552, February.
    5. Tomáš Vetrík & Selvaraj Balachandran, 2020. "General multiplicative Zagreb indices of trees and unicyclic graphs with given matching number," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 953-973, November.
    6. Zheng, Ruiling & Su, Peifeng & Jin, Xian’an, 2023. "Arithmetic-geometric matrix of graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 442(C).
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