2-Tuple Total Domination Number in Circulant Graphs
نویسنده
چکیده
In this paper, a necessary and sufficient condition for the existence of an efficient 2-dominating set in a class of circulant graphs has been obtained and for those circulant graphs, an upper bound for the 2domination number is also obtained. For the circulant graphs Cir(n,A), where A = {1, 2, . . . , x, n − 1, n − 2, . . . , n − x} and x ≤ bn−1 2 c, the perfect 2-tuple total domination number γ×2t has been studied. Also some 2-tuple total dominating 2-excellent circulant graphs and 2-tuple total dominating 2-restricted circulant graphs are identified. It is proved that any subgroup of the finite cyclic group Zn can be a perfect 2-tuple total dominating set of Cir(n,A) for some generating set A. Mathematics Subject Classification: 05C69
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