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On total {k}-domatic number of Cartesian and direct product of graphs

Funds:  Supported by NNSF of China (11671376, 11401004), Anhui Provincial Natural Science Foundation (1708085MA18).
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https://doi.org/10.3969/j.issn.0253-2778.2018.08.001
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  • Author Bio:

    LIANG Yong, male, born in 1981, master. Research field: Graph theory. E-mail: Liangy@ mail.ustc.edu.cn

  • Corresponding author: HU Futao
  • Received Date: 07 July 2017
  • Accepted Date: 01 December 2017
  • Rev Recd Date: 01 December 2017
  • Publish Date: 31 August 2018
    Abstract

  • Abstract

    For a positive integer k, the total {k}-dominating function (T{k} DF) of a graph G without isolated vertices is a function f from the vertex set V(G) to

    Abstract

    For a positive integer k, the total {k}-dominating function (T{k} DF) of a graph G without isolated vertices is a function f from the vertex set V(G) to
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    • References(6)
  • [1]
    XU J M. Theory and Application of Graphs[M]. Dordrecht/ Boston/ London: Kluwer Academic Publishers, 2003.
    [2]
    COCKAYNE E J, DAWES R M, HEDETNIEMI S T. Total domination in graphs[J]. Networks, 1980, 10: 211-219.
    [3]
    LI N, HOU X. On the total {k}-domination number of Cartesian products of graphs[J]. J Comb Optim, 2009, 18: 173-178.
    [4]
    SHEIKHOLESLAMI S M, VOLKMANN L. The total k-domatic number of a graph[J]. J Comb Optim, 2012, 23: 252-260.
    [5]
    CHEN J, HOU X, LI N. The total k-domatic number of wheels and complete graphs[J]. J Comb Optim, 2012, 24: 162-175.
    [6]
    ARAM H, SHEIKHOLESLAMI S M, VOLMANN L. On the total {k}-domination and total {k}-domatic number of graphs[J]. Bull Malays Math Sci Soc, 2013, 36: 39-47.)
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    [1]
    XU J M. Theory and Application of Graphs[M]. Dordrecht/ Boston/ London: Kluwer Academic Publishers, 2003.
    [2]
    COCKAYNE E J, DAWES R M, HEDETNIEMI S T. Total domination in graphs[J]. Networks, 1980, 10: 211-219.
    [3]
    LI N, HOU X. On the total {k}-domination number of Cartesian products of graphs[J]. J Comb Optim, 2009, 18: 173-178.
    [4]
    SHEIKHOLESLAMI S M, VOLKMANN L. The total k-domatic number of a graph[J]. J Comb Optim, 2012, 23: 252-260.
    [5]
    CHEN J, HOU X, LI N. The total k-domatic number of wheels and complete graphs[J]. J Comb Optim, 2012, 24: 162-175.
    [6]
    ARAM H, SHEIKHOLESLAMI S M, VOLMANN L. On the total {k}-domination and total {k}-domatic number of graphs[J]. Bull Malays Math Sci Soc, 2013, 36: 39-47.)
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