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Graph distance measures based on topological indices revisited

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  • Dehmer, Matthias
  • Emmert-Streib, Frank
  • Shi, Yongtang

Abstract

Graph distance measures based on topological indices have been already explored by Dehmer et al. Also, inequalities for those graph distance measures have been proved. In this paper, we continue studying such comparative graph measures based on the well-known Wiener index, graph energy and Randić index, respectively. We prove extremal properties of the graph distance measures for some special classes of graphs. To demonstrate useful properties of the measures, we also discuss numerical results. To conclude the paper we state some open problems.

Suggested Citation

  • Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:623-633
    DOI: 10.1016/j.amc.2015.05.072
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    References listed on IDEAS

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    1. Wilhelm, Thomas & Hollunder, Jens, 2007. "Information theoretic description of networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 385-396.
    2. Matthias Dehmer & Frank Emmert-Streib & Shailesh Tripathi, 2013. "Large-Scale Evaluation of Molecular Descriptors by Means of Clustering," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-10, December.
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    Cited by:

    1. Yu, Guihai & Li, Xingfu, 2020. "Connective Steiner 3-eccentricity index and network similarity measure," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Ghorbani, Modjtaba & Dehmer, Matthias & Rajabi-Parsa, Mina & Emmert-Streib, Frank & Mowshowitz, Abbe, 2019. "Hosoya entropy of fullerene graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 88-98.
    3. Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2020. "Properties of Entropy-Based Topological Measures of Fullerenes," Mathematics, MDPI, vol. 8(5), pages 1-23, May.
    4. Ghorbani, Modjtaba & Dehmer, Matthias & Zangi, Samaneh, 2018. "Graph operations based on using distance-based graph entropies," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 547-555.
    5. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    6. Das, Kinkar Ch. & Gutman, Ivan & Nadjafi–Arani, Mohammad J., 2015. "Relations between distance–based and degree–based topological indices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 142-147.
    7. Choi, Hayoung & Lee, Hosoo & Shen, Yifei & Shi, Yuanming, 2019. "Comparing large-scale graphs based on quantum probability theory," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 1-15.
    8. Maryam Jalali-Rad & Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2021. "Orbit Entropy and Symmetry Index Revisited," Mathematics, MDPI, vol. 9(10), pages 1-13, May.
    9. Liu, Muhuo & Das, Kinkar Ch., 2018. "On the ordering of distance-based invariants of graphs," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 191-201.
    10. Ghorbani, Modjtaba & Hakimi-Nezhaad, Mardjan & Dehmer, Matthias, 2022. "Novel results on partial hosoya polynomials: An application in chemistry," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    11. Ilić, Aleksandar & Ilić, Milovan, 2017. "Counterexamples to conjectures on graph distance measures based on topological indexes," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 148-152.

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