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.