Improved Upper Bound on Independent Domination Number for Hypercubes

05/13/2022

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by   Debabani Chowdhury, et al.

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We revisit the problem of determining the independent domination number in hypercubes for which the known upper bound is still not tight for general dimensions. We present here a constructive method to build an independent dominating set S_n for the n-dimensional hypercube Q_n, where n=2p+1, p being a positive integer ≥ 1, provided an independent dominating set S_p for the p-dimensional hypercube Q_p, is known. The procedure also computes the minimum independent dominating set for all n=2^k-1, k>1. Finally, we establish that the independent domination number α_n≤ 3 × 2^n-k-2 for 7× 2^k-2-1≤ n<2^k+1-1, k>1. This is an improved upper bound for this range as compared to earlier work.