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On the Signed Domination Number of the Cartesian Product of Two Directed Cycles

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DOI: 10.4236/ojdm.2015.53005    3,794 Downloads   4,619 Views   Citations
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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.

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Shaheen, R. (2015) On the Signed Domination Number of the Cartesian Product of Two Directed Cycles. Open Journal of Discrete Mathematics, 5, 54-64. doi: 10.4236/ojdm.2015.53005.


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