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RETRACTED ARTICLE: The Sachs theorem and its application on extended adjacency matrix of graphs

Author

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  • Bo Deng

    (Qinghai Normal University
    Academy of Plateau Science and Sustainability
    The State Key Laboratory of Tibetan Information Processing and Application)

  • Caibing Chang

    (Qinghai Normal University)

  • Kinkar Chandra Das

    (Sungkyunkwan University)

Abstract

Based on the extended adjacency matrix, the spectral radius and the energy of the extended adjacency matrix are found that they possess high discriminating power and correlate well with a number of physicochemical properties and biological activities of organic compounds. In this research, by establishing a relationship between directed graphs and undirected graphs, we mainly present the Sachs theorem and the Coulson’s integral formula of the energy of the extended adjacency matrix of G. By using the formula, we can compare the energies of the extended adjacency matrices of two graphs and we find that the graph energy is less than the extended energy in the case of a tree.

Suggested Citation

  • 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 "RETRACTED ARTICLE: The Sachs theorem and its application on extended adjacency matrix of graphs," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-12,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.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00938-y
    DOI: 10.1007/s10878-022-00938-y
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    References listed on IDEAS

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    1. Das, Kinkar Ch. & Gutman, Ivan & Furtula, Boris, 2017. "On spectral radius and energy of extended adjacency matrix of graphs," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 116-123.
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    Cited by:

    1. 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.

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