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- W4280491571 abstract "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 $ge 1$, 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 $alpha_nleq 3 times 2^{n-k-2}$ for $7times 2^{k-2}-1leq n<2^{k+1}-1$, $k>1$. This is an improved upper bound for this range as compared to earlier work." @default.
- W4280491571 created "2022-05-22" @default.
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- W4280491571 date "2022-05-13" @default.
- W4280491571 modified "2023-09-30" @default.
- W4280491571 title "Improved Upper Bound on Independent Domination Number for Hypercubes" @default.
- W4280491571 doi "https://doi.org/10.48550/arxiv.2205.06671" @default.
- W4280491571 hasPublicationYear "2022" @default.
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