IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i8p1265-d393414.html
   My bibliography  Save this article

Strong Edge Coloring of Generalized Petersen Graphs

Author

Listed:
  • Ming Chen

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China)

  • Lianying Miao

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China)

  • Shan Zhou

    (School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China)

Abstract

A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph P ( n , k ) with k ≥ 4 and n > 2 k can be strong edge colored with (at most) seven colors. Although the generalized Petersen graph P ( n , k ) is a kind of special graph, the strong chromatic index of P ( n , k ) is still unknown. In this paper, we support the conjecture by showing that the strong chromatic index of every generalized Petersen graph P ( n , k ) with k ≥ 4 and n > 2 k is at most 9.

Suggested Citation

  • Ming Chen & Lianying Miao & Shan Zhou, 2020. "Strong Edge Coloring of Generalized Petersen Graphs," Mathematics, MDPI, vol. 8(8), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1265-:d:393414
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/8/1265/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/8/1265/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yang, Zixuan & Wu, Baoyindureng, 2018. "Strong edge chromatic index of the generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 431-441.
    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. David G. L. Wang & Monica M. Y. Wang & Shiqiang Zhang, 2022. "Determining the edge metric dimension of the generalized Petersen graph P(n, 3)," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 460-496, March.
    2. Lily Chen & Shumei Chen & Ren Zhao & Xiangqian Zhou, 2020. "The strong chromatic index of graphs with edge weight eight," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 227-233, July.

    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:gam:jmathe:v:8:y:2020:i:8:p:1265-:d:393414. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.