IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v43y2012i6d10.1007_s13226-012-0038-8.html
   My bibliography  Save this article

On bounds for the cutting number of a graph

Author

Listed:
  • Simon Mukwembi

    (University of KwaZulu-Natal, Westville Campus)

  • Senelani Dorothy Hove-Musekwa

    (National University of Science and Technology)

Abstract

The cutting number of a vertex v of a finite graph G = (V,E) is a natural measure of the extent to which the removal of v disconnects the graph. Precisely, the cutting number c(v) of v is defined as the number of pairs of vertices {u,w} of G such that u,w ≠ v and every u-w path contains v. The cutting number c(G) of G is the maximum value of c(v) over all vertices in V. We provide exact bounds on the cutting number of G in terms of order and diameter of the graph.

Suggested Citation

  • Simon Mukwembi & Senelani Dorothy Hove-Musekwa, 2012. "On bounds for the cutting number of a graph," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(6), pages 637-649, December.
    • Handle: RePEc:spr:indpam:v:43:y:2012:i:6:d:10.1007_s13226-012-0038-8
    DOI: 10.1007/s13226-012-0038-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-012-0038-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-012-0038-8?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    Full references (including those not matched with items on IDEAS)

    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. De Masi, G. & Giovannetti, G. & Ricchiuti, G., 2013. "Network analysis to detect common strategies in Italian foreign direct investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1202-1214.
    2. Fogel, Kathy & Jandik, Tomas & McCumber, William R., 2018. "CFO social capital and private debt," Journal of Corporate Finance, Elsevier, vol. 52(C), pages 28-52.
    3. van den Brink, René & Rusinowska, Agnieszka, 2024. "Degree centrality, von Neumann–Morgenstern expected utility and externalities in networks," European Journal of Operational Research, Elsevier, vol. 319(2), pages 669-677.
    4. repec:hal:pseptp:halshs-04188289 is not listed on IDEAS
    5. Liu, Qiuling & Guo, Lei & Sun, Yiping & Ren, Linlin & Wang, Xinhua & Han, Xiaohui, 2024. "Do scholars' collaborative tendencies impact the quality of their publications? A generalized propensity score matching analysis," Journal of Informetrics, Elsevier, vol. 18(1).
    6. Wouter van den Bos & Eveline A Crone & Rosa Meuwese & Berna Güroğlu, 2018. "Social network cohesion in school classes promotes prosocial behavior," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-16, April.
    7. Hongxing Yao & Yanyu Lu & Bilal Ahmed Memon, 2019. "Impact of US-China Trade War on the Network Topology Structure of Chinese Stock Market," Journal of Asian Business Strategy, Asian Economic and Social Society, vol. 9(2), pages 235-250, December.
    8. Hyuk-Soo Kwon & Jihong Lee & Sokbae Lee & Ryungha Oh, 2022. "Knowledge spillovers and patent citations: trends in geographic localization, 1976–2015," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 31(3), pages 123-147, April.
    9. Ding, Yueting & Zhang, Ming & Chen, Sai & Nie, Rui, 2020. "Assessing the resilience of China’s natural gas importation under network disruptions," Energy, Elsevier, vol. 211(C).
    10. Liu, Ying & Tang, Ming & Zhou, Tao & Do, Younghae, 2016. "Identify influential spreaders in complex networks, the role of neighborhood," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 289-298.
    11. Mengying Cui & David Levinson, 2018. "Accessibility analysis of risk severity," Transportation, Springer, vol. 45(4), pages 1029-1050, July.
    12. Zhang, Xiaohang & Cui, Huiyuan & Zhu, Ji & Du, Yu & Wang, Qi & Shi, Wenhua, 2017. "Measuring the dissimilarity of multiplex networks: An empirical study of international trade networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 380-394.
    13. Zheng, Wei & Wei, Sheng, 2024. "A ‘node-place-network-city’ framework to examine HSR station area development dynamics: Station typologies and development strategies," Journal of Transport Geography, Elsevier, vol. 120(C).
    14. Fang, Ming & Francis, Bill & Hasan, Iftekhar & Wu, Qiang, 2022. "External social networks and earnings management," The British Accounting Review, Elsevier, vol. 54(2).
    15. Mario V. Tomasello & Mauro Napoletano & Antonios Garas & Frank Schweitzer, 2017. "The rise and fall of R&D networks," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 26(4), pages 617-646.
    16. Lee, Byoung-Hwa & Jung, Woo-Sung, 2018. "Analysis on the urban street network of Korea: Connections between topology and meta-information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 15-25.
    17. Tao, Qizhi & Li, Haoyu & Wu, Qun & Zhang, Ting & Zhu, Yingjun, 2019. "The dark side of board network centrality: Evidence from merger performance," Journal of Business Research, Elsevier, vol. 104(C), pages 215-232.
    18. Barthelemy, J. P. & Bisdorff, R. & Coppin, G., 2002. "Human centered processes and decision support systems," European Journal of Operational Research, Elsevier, vol. 136(2), pages 233-252, January.
    19. Papa, Enrica & Bertolini, Luca, 2015. "Accessibility and Transit-Oriented Development in European metropolitan areas," Journal of Transport Geography, Elsevier, vol. 47(C), pages 70-83.
    20. Yang, Xu-Hua & Xiong, Zhen & Ma, Fangnan & Chen, Xiaoze & Ruan, Zhongyuan & Jiang, Peng & Xu, Xinli, 2021. "Identifying influential spreaders in complex networks based on network embedding and node local centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    21. repec:dau:papers:123456789/7616 is not listed on IDEAS
    22. Mahendra Piraveenan & Mikhail Prokopenko & Liaquat Hossain, 2013. "Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-14, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:indpam:v:43:y:2012:i:6:d:10.1007_s13226-012-0038-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.