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On adjacency-distance spectral radius and spread of graphs

Author

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  • Guo, Haiyan
  • Zhou, Bo

Abstract

Let G be a connected graph. The greatest eigenvalue and the spread of the sum of the adjacency matrix and the distance matrix of G are called the adjacency-distance spectral radius and the adjacency-distance spread of G, respectively. Both quantities are used as molecular descriptors in chemoinformatics. We establish some properties for the adjacency-distance spectral radius and the adjacency-distance spread by proposing local grafting operations such that the adjacency-distance spectral radius is decreased or increased. Hence, we characterize those graphs that uniquely minimize and maximize the adjacency-distance spectral radii in several sets of graphs, and determine trees with small adjacency-distance spreads. It transpires that the adjacency-distance spectral radius satisfies the requirements of a branching index.

Suggested Citation

  • Guo, Haiyan & Zhou, Bo, 2020. "On adjacency-distance spectral radius and spread of graphs," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308112
    DOI: 10.1016/j.amc.2019.124819
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    Cited by:

    1. Maryam Baghipur & Modjtaba Ghorbani & Shariefuddin Pirzada & Najaf Amraei, 2023. "On the Generalized Adjacency Spread of a Graph," Mathematics, MDPI, vol. 11(6), pages 1-9, March.

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