A Note on the 2-Tuple Total Domination Problem in Harary Graphs

摘要

Let G be a graph with minimum degree at least 2. A vertex subset S is a 2-tuple total dominating set of G if every vertex is adjacent to at least two vertices in S. The 2-tuple total domination number of G is the minimum size of a 2-tuple total dominating set. In this paper, we are concerned with the 2-tuple total domination number of a Harary graph H2m+1, 2n+1 with 2n+1 = (2m+1)ℓ. For m = 1 and m = 2, we show that the numbers are 2ℓ and 2ℓ+1, respectively.