• Corpus ID: 35421753

On Independent and ( d , n )-domination numbers of hypercubes

@inproceedings{Mane2012OnIA,
  title={On Independent and ( d , n )-domination numbers of hypercubes},
  author={S. A. Mane and B. N. Waphare},
  year={2012}
}
In this paper we consider the (d, n)-domination number, γd,n(Qn), the distance-d domination number γd(Qn) and the connected distance-d domination number γc,d(Qn) of ndimensional hypercube graphs Qn. We show that for 2 ≤ d ≤ bn/2c, and n ≥ 4, γd,n(Qn) ≤ 2n−2d+2, improving the bound of Xie and Xu [19]. We also show that γd(Qn) ≤ 2n−2d+2−r, for 2 − 1 ≤ n − 2d + 1 < 2 − 1, and γc,d(Qn) ≤ 2n−d, for 1 ≤ n− d + 1 ≤ 3, and γc,d(Qn) ≤ 2n−d−1 + 4, for n− d + 1 ≥ 4. Moreover, we give an upper bound of the… 
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