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

Ramy Shaheen^*

Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria.

DOI: 10.4236/ojdm.2015.53005                

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 C_m × C_n denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of g_s(C_m × C_n) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of g_s(C_m × C_n) when m,  (mod 3) and bounds for otherwise.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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