IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v24y2012i3d10.1007_s10878-011-9412-4.html
   My bibliography  Save this article

Minimum statuses of connected graphs with fixed maximum degree and order

Author

Listed:
  • Chiang Lin

    (National Central University)

  • Wei-Han Tsai

    (National Central University)

  • Jen-Ling Shang

    (Kainan University)

  • Yuan-Jen Zhang

    (National Central University)

Abstract

The status of a vertex in a connected graph is the sum of distances between the vertex and all vertices. The minimum status of a connected graph is the minimum of statuses of all vertices of this graph. In this paper we obtain the sharp lower bound and the sharp upper bound on the minimum status of a connected graph with maximum degree k and order n. All the graphs attaining the lower bound are obtained, and a necessary condition is given for those graphs attaining the upper bound.

Suggested Citation

  • Chiang Lin & Wei-Han Tsai & Jen-Ling Shang & Yuan-Jen Zhang, 2012. "Minimum statuses of connected graphs with fixed maximum degree and order," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 147-161, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9412-4
    DOI: 10.1007/s10878-011-9412-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-011-9412-4
    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/s10878-011-9412-4?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. A. J. Goldman, 1972. "Minimax Location of a Facility in a Network," Transportation Science, INFORMS, vol. 6(4), pages 407-418, November.
    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. Lin, Hongying & Zhou, Bo, 2021. "Which numbers are status differences?," Applied Mathematics and Computation, Elsevier, vol. 399(C).

    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. Mulder, H.M. & Pelsmajer, M.J. & Reid, K.B., 2006. "Generalized centrality in trees," Econometric Institute Research Papers EI 2006-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Joseph S. Martinich, 1988. "A vertex‐closing approach to the p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 185-201, April.
    3. Jesús Muñuzuri & Pablo Cortés & Rafael Grosso & Luis Onieva, 2016. "Teaching Heuristic Methods to Industrial Engineers: A Problem-Based Experience," INFORMS Transactions on Education, INFORMS, vol. 16(2), pages 60-67, January.
    4. ReVelle, C.S. & Eiselt, H.A. & Daskin, M.S., 2008. "A bibliography for some fundamental problem categories in discrete location science," European Journal of Operational Research, Elsevier, vol. 184(3), pages 817-848, February.
    5. Lin, Hongying & Zhou, Bo, 2021. "Which numbers are status differences?," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    6. Hyunwoo Lim & Narushige Shiode, 2011. "Parcel Distribution Networks for Online Shopping Business," Chapters, in: Kenneth Button & Aura Reggiani (ed.), Transportation and Economic Development Challenges, chapter 6, Edward Elgar Publishing.
    7. Wei Ding & Ke Qiu, 2017. "An FPTAS for generalized absolute 1-center problem in vertex-weighted graphs," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1084-1095, November.
    8. Wei Ding & Ke Qiu & Yu Zhou & Zhou Ye, 2022. "A sifting-edges algorithm for accelerating the computation of absolute 1-center in graphs," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 905-920, September.

    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:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9412-4. 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.