2022/05/13 by Chowdhury, Debabani, Das, Debesh K., Bhattacharya, Bhargab B.
#05 #06 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2 #G.m
paper · doi:10.48550/arxiv.2205.06671
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 Sn for the n-dimensional hypercube Qn, where n=2p+1, p being a positive integer ≥ 1, provided an independent dominating set Sp for the p-dimensional hypercube Qp, is known. The procedure also computes the minimum independent dominating set for all n=2k-1, k>1. Finally, we establish that the independent domination number αn≤ 3 × 2n-k-2 for 7× 2k-2-1≤ n<2k+1-1, k>1. This is an improved upper bound for this range as compared to earlier work.