Total Domination Number of Cartesian Product of Cycles Cm Cn For m = 6, 7

Authors:

M. Thiagarajan (Madurai Kamaraj University, Madurai)

R. Bhaskaram (Madurai Kamaraj University, Madurai)

Keywords: Cartesian Product, Total dominating set, Total domination number.

Abstract:

Let G = (V, E) be a graph. A set of vertices S ⊂ V is called a total dominating set of G if every vertex of G is adjacent to some vertex in S. The total domination number γt (G) of a graph G is the cardinality of a minimum total dominating set. In this paper, we enumerate the method of constructing a minimum total dominating set and thereby determine the total domination number γt (Cm Cn) for cartesian product of cycles Cm Cn for any n and m = AMS 6 and 7.

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