IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v31y2016i2d10.1007_s10878-014-9796-z.html
   My bibliography  Save this article

Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs

Author

Listed:
  • Yi Wang

    (Anhui University)

  • Jian Cheng

    (West Virginia University)

  • Rong Luo

    (West Virginia University)

  • Gregory Mulley

    (West Virginia University)

Abstract

The adjacent vertex-distinguishing chromatic index $$\chi '_{avd}(G)$$ χ a v d ′ ( G ) of a graph $$G$$ G is the smallest integer $$k$$ k for which $$G$$ G admits a proper edge $$k$$ k -coloring such that no pair of adjacent vertices are incident with the same set of colors. In this paper, we prove that if $$G$$ G is a $$2$$ 2 -degenerate graph without isolated edges, then $$\chi '_{avd} (G)\le \max \{6, \Delta (G)+1\}$$ χ a v d ′ ( G ) ≤ max { 6 , Δ ( G ) + 1 } . Moreover, we also show that when $$\Delta \ge 6$$ Δ ≥ 6 , $$\chi '_{avd}= \Delta (G)+1$$ χ a v d ′ = Δ ( G ) + 1 if and only if $$G$$ G contains two adjacent vertices of maximum degree.

Suggested Citation

  • Yi Wang & Jian Cheng & Rong Luo & Gregory Mulley, 2016. "Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 874-880, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9796-z
    DOI: 10.1007/s10878-014-9796-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9796-z
    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/s10878-014-9796-z?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. Hervé Hocquard & Mickaël Montassier, 2013. "Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 152-160, July.
    2. Weifan Wang & Yiqiao Wang, 2010. "Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 471-485, May.
    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. Jingjing Yao & Xiaowei Yu & Guanghui Wang & Changqing Xu, 2017. "Neighbor sum distinguishing total coloring of 2-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 64-70, July.
    2. Xiaolan Hu & Yaojun Chen & Rong Luo & Zhengke Miao, 2017. "Neighbor sum distinguishing index of 2-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 798-809, October.
    3. Junlei Zhu & Yuehua Bu & Yun Dai, 2018. "Upper bounds for adjacent vertex-distinguishing edge coloring," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 454-462, February.

    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. Junlei Zhu & Yuehua Bu & Yun Dai, 2018. "Upper bounds for adjacent vertex-distinguishing edge coloring," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 454-462, February.
    2. Joanna Skowronek-Kaziów, 2017. "Graphs with multiplicative vertex-coloring 2-edge-weightings," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 333-338, January.
    3. Chengchao Yan & Danjun Huang & Dong Chen & Weifan Wang, 2014. "Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 893-909, November.
    4. Zhuoya Liu & Changqing Xu, 2022. "Adjacent vertex distinguishing edge coloring of IC-planar graphs," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 710-726, May.
    5. Jingjing Huo & Yiqiao Wang & Weifan Wang, 2017. "Neighbor-sum-distinguishing edge choosability of subcubic graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 742-759, October.
    6. Zengtai Gong & Chen Zhang, 2023. "Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs," Mathematics, MDPI, vol. 11(10), pages 1-25, May.
    7. Huijuan Wang & Lidong Wu & Weili Wu & Jianliang Wu, 2014. "Minimum number of disjoint linear forests covering a planar graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 274-287, July.
    8. Hervé Hocquard & Mickaël Montassier, 2013. "Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 152-160, 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:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9796-z. 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.