IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v259y2015icp470-479.html
   My bibliography  Save this article

Novel inequalities for generalized graph entropies – Graph energies and topological indices

Author

Listed:
  • Li, Xueliang
  • Qin, Zhongmei
  • Wei, Meiqin
  • Gutman, Ivan
  • Dehmer, Matthias

Abstract

The entropy of a graph is an information-theoretic quantity for measuring the complexity of a graph. After Shannon introduced the entropy to information and communication, many generalizations of the entropy measure have been proposed, such as Rényi entropy and Daróczy entropy. In this article, we prove accurate connections (inequalities) between generalized graph entropies, graph energies, and topological indices. Additionally, we obtain some extremal properties of nine generalized graph entropies by employing graph energies and topological indices.

Suggested Citation

  • Li, Xueliang & Qin, Zhongmei & Wei, Meiqin & Gutman, Ivan & Dehmer, Matthias, 2015. "Novel inequalities for generalized graph entropies – Graph energies and topological indices," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 470-479.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:470-479
    DOI: 10.1016/j.amc.2015.02.059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315002520
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.02.059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    2. Mukwembi, Simon, 2011. "Effects of density of infected population to the spreading of HIV epidemic in communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3915-3921.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2015. "An inequality between the edge-Wiener index and the Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 714-721.
    2. Milovanović, Igor & Milovanović, Emina & Gutman, Ivan, 2016. "Upper bounds for some graph energies," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 435-443.
    3. Das, Kinkar Ch. & Mojallal, Seyed Ahmad & Gutman, Ivan, 2016. "On energy and Laplacian energy of bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 759-766.
    4. Safaei, F. & Yeganloo, H. & Akbar, R., 2020. "Robustness on topology reconfiguration of complex networks: An entropic approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 379-409.
    5. Das, Kinkar Ch. & Mojallal, Seyed Ahmad, 2016. "Extremal Laplacian energy of threshold graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 267-280.
    6. 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.
    7. Li, Hong-Hai & Wu, Qian-Qian & Gutman, Ivan, 2016. "On ordering of complements of graphs with respect to matching numbers," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 167-174.
    8. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    9. Das, Kinkar Ch. & Mojallal, Seyed Ahmad & Gutman, Ivan, 2015. "On Laplacian energy in terms of graph invariants," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 83-92.
    10. Rodríguez, José M. & Sigarreta, José M., 2016. "Spectral properties of geometric–arithmetic index," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 142-153.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Konno, Tomohiko, 2013. "An imperfect competition on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5453-5460.
    2. R. Bentley & Michael O’Brien & Paul Ormerod, 2011. "Quality versus mere popularity: a conceptual map for understanding human behavior," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 10(2), pages 181-191, December.
    3. Xiang Wei & Peng Xu & Shuiting Du & Guanghui Yan & Huayan Pei, 2021. "Reputational preference-based payoff punishment promotes cooperation in spatial social dilemmas," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(10), pages 1-7, October.
    4. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "The effect of individual attitude on cooperation in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    5. Lv, Shaojie & Song, Feifei, 2022. "Particle swarm intelligence and the evolution of cooperation in the spatial public goods game with punishment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Wu, Jieyu & Shao, Xinyu & Li, Jinhang & Huang, Gang, 2012. "Scale-free properties of information flux networks in genetic algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1692-1701.
    7. Benjamin Allen & Christine Sample & Robert Jencks & James Withers & Patricia Steinhagen & Lori Brizuela & Joshua Kolodny & Darren Parke & Gabor Lippner & Yulia A Dementieva, 2020. "Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-20, January.
    8. K. Kułakowski, 2009. "The norm game: punishing enemies and not friends," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 4(1), pages 27-37, June.
    9. Zhang, Hui & Wang, Li & Hou, Dongshuang, 2016. "Effect of the spatial autocorrelation of empty sites on the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 296-308.
    10. Huo, Ran & Durrett, Rick, 2018. "Latent voter model on locally tree-like random graphs," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1590-1614.
    11. Antoine Nongaillard & Philippe Mathieu, 2011. "Reallocation Problems in Agent Societies: A Local Mechanism to Maximize Social Welfare," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 14(3), pages 1-5.
    12. Laura Schmid & Farbod Ekbatani & Christian Hilbe & Krishnendu Chatterjee, 2023. "Quantitative assessment can stabilize indirect reciprocity under imperfect information," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    13. Feng, Sinan & Liu, Xuesong & Dong, Yida, 2022. "Limited punishment pool may promote cooperation in the public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    14. Wakano, Joe Yuichiro & Ohtsuki, Hisashi & Kobayashi, Yutaka, 2013. "A mathematical description of the inclusive fitness theory," Theoretical Population Biology, Elsevier, vol. 84(C), pages 46-55.
    15. Tetsushi Ohdaira, 2021. "Cooperation evolves by the payoff-difference-based probabilistic reward," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-8, November.
    16. Bryant, Adam S. & Lavrentovich, Maxim O., 2022. "Survival in branching cellular populations," Theoretical Population Biology, Elsevier, vol. 144(C), pages 13-23.
    17. McAvoy, Alex & Fraiman, Nicolas & Hauert, Christoph & Wakeley, John & Nowak, Martin A., 2018. "Public goods games in populations with fluctuating size," Theoretical Population Biology, Elsevier, vol. 121(C), pages 72-84.
    18. Jonas I Liechti & Gabriel E Leventhal & Sebastian Bonhoeffer, 2017. "Host population structure impedes reversion to drug sensitivity after discontinuation of treatment," PLOS Computational Biology, Public Library of Science, vol. 13(8), pages 1-19, August.
    19. Qiguang An & Hongfeng Guo & Yating Zheng, 2022. "On Robust Stability and Stabilization of Networked Evolutionary Games with Time Delays," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    20. Pi, Jinxiu & Wang, Chun & Zhou, Die & Tang, Wei & Yang, Guanghui, 2024. "Evolutionary dynamics of N-person snowdrift game with two thresholds in well-mixed and structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:470-479. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.