On the Signed Domination Number of the Cartesian Product of Two Directed Cycles - Open Journal of Discrete Mathematics

OJDM > Vol.5 No.3, July 2015

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

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DOI: 10.4236/ojdm.2015.53005 4,240 Downloads 5,639 Views Citations

Author(s)

Ramy Shaheen^*

Affiliation(s)

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

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

Share and Cite:

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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