OJDM  Vol.5 No.3 , July 2015
On the Signed Domination Number of the Cartesian Product of Two Directed Cycles
Author(s) Ramy Shaheen*
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.

Cite this paper
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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