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Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers

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  • Patcharapan Jumnongnit
  • Kittikorn Nakprasit

Abstract

Let be a graph and be a -total coloring. Let denote the sum of color on a vertex and colors assigned to edges incident to . If whenever , then is called a neighbor sum distinguishing total coloring. The smallest integer such that has a neighbor sum distinguishing -total coloring is denoted by . In 2014, Dong and Wang obtained the results about depending on the value of maximum average degree. A -assignment of is a list assignment of integers to vertices and edges with for each vertex and for each edge . A total- -coloring is a total coloring of such that whenever and whenever . We state that has a neighbor sum distinguishing total- -coloring if has a total- -coloring such that for all . The smallest integer such that has a neighbor sum distinguishing total- -coloring for every -assignment is denoted by . In this paper, we strengthen results by Dong and Wang by giving analogous results for .

Suggested Citation

  • Patcharapan Jumnongnit & Kittikorn Nakprasit, 2017. "Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-4, November.
    • Handle: RePEc:hin:jijmms:5897049
    DOI: 10.1155/2017/5897049
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    References listed on IDEAS

    as
    1. Cunquan Qu & Guanghui Wang & Guiying Yan & Xiaowei Yu, 2016. "Neighbor sum distinguishing total choosability of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 906-916, October.
    2. Hualong Li & Laihao Ding & Bingqiang Liu & Guanghui Wang, 2015. "Neighbor sum distinguishing total colorings of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 675-688, October.
    3. Weifan Wang & Danjun Huang, 2014. "The adjacent vertex distinguishing total coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 379-396, February.
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