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On maximum Zagreb connection indices for trees with fixed domination number

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  • Raza, Zahid
  • Akhter, Shehnaz

Abstract

The Zagreb connection indices of a graph are notable topological descriptors constructed from the connection number of every vertex (cardinality of set of vertices with distance two from that vertex). In 1972, these indices were presented to determine the total electron energy of the alternate hydrocarbons. The Zagreb connection indices give finer values for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers compared to basic Zagreb indices. For many years, all these connection indices have been ignored by researchers for further work. Recently, determining the extremal bounds for the topological indices in terms of graph parameters has turned out to be an interesting direction in extremal graph theory, and numerous related results have been acquired in the literature. This article presents sharp bounds on the first, second, and modified Zagreb connection indices of trees with a fixed domination number. These bounds are strict, and the trees which attained these bounds are characterized.

Suggested Citation

  • Raza, Zahid & Akhter, Shehnaz, 2023. "On maximum Zagreb connection indices for trees with fixed domination number," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001431
    DOI: 10.1016/j.chaos.2023.113242
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    References listed on IDEAS

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    1. Jinde Cao & Usman Ali & Muhammad Javaid & Chuangxia Huang, 2020. "Zagreb Connection Indices of Molecular Graphs Based on Operations," Complexity, Hindawi, vol. 2020, pages 1-15, March.
    2. Yousaf, Shamaila & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2022. "On total irregularity index of trees with given number of segments or branching vertices," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Sadia Noureen & Akhlaq Ahmad Bhatti & Akbar Ali, 2020. "Extremum Modified First Zagreb Connection Index of - Vertex Trees with Fixed Number of Pendent Vertices," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-6, April.
    4. Borovićanin, Bojana & Furtula, Boris, 2016. "On extremal Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 208-218.
    5. Haiying Wang & Jia-Bao Liu & Shaohui Wang & Wei Gao & Shehnaz Akhter & Muhammad Imran & Mohammad R. Farahani, 2017. "Sharp Bounds for the General Sum-Connectivity Indices of Transformation Graphs," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, December.
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