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Note on the perfect EIC-graphs

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  • Yue, Jun
  • Zhang, Shiliang
  • Zhang, Xia

Abstract

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The injective edge coloring number χi′(G) is the minimum number of colors permitted in a coloring of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then e1 and e3 receive the different colors. Let ω′ denote the number of edges in a maximum clique of G. A graph G is called an ω′ edge injective colorable (or perfect EIC-)graph if χi′(G)=ω′. In this paper, we give a sharp bound of the injective coloring number of a 2-connected graph with some forbidden conditions, and then we also characterize some perfect EIC-graph classes, which extends the results of perfect EIC-graph of Cardoso et al. in [Injective edge chromatic index of a graph, http://arxiv.org/abs/1510.02626.].

Suggested Citation

  • Yue, Jun & Zhang, Shiliang & Zhang, Xia, 2016. "Note on the perfect EIC-graphs," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 481-485.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:481-485
    DOI: 10.1016/j.amc.2016.05.031
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    References listed on IDEAS

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    1. Li, Shasha & Li, Xueliang & Shi, Yongtang, 2015. "Note on the complexity of deciding the rainbow (vertex-) connectedness for bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 155-161.
    2. Min Chen & Geňa Hahn & André Raspaud & Weifan Wang, 2012. "Some results on the injective chromatic number of graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 299-318, October.
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    Cited by:

    1. Yue, Jun & Wei, Meiqin & Li, Min & Liu, Guodong, 2018. "On the double Roman domination of graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 669-675.

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