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Karami, H., Sheikholeslami, S.M. and Khodkar, A. (2009) Lower Bounds on the Signed Domination Numbers of Directed Graphs. Discrete Mathematics, 309, 2567-2570.
http://dx.doi.org/10.1016/j.disc.2008.04.001

has been cited by the following article:

• TITLE: On the Signed Domination Number of the Cartesian Product of Two Directed Cycles

  AUTHORS: Ramy Shaheen

  KEYWORDS: Directed Graph, Directed Cycle, Cartesian Product, Signed Dominating Function, Signed Domination Number

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.5 No.3, July 24, 2015

  ABSTRACT: Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function is called a signed dominating function (SDF) if for each vertex . The weight of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, (mod 3) and bounds for otherwise.