Improved Upper Bound on Independent Domination Number for Hypercubes

Autor:	Chowdhury, Debabani, Das, Debesh K., Bhattacharya, Bhargab B.
Rok vydání:	2022
Předmět:	Computer Science - Discrete Mathematics Mathematics - Combinatorics 05 06 G.2 G.m
Druh dokumentu:	Working Paper
Popis:	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 $\alpha_n\leq 3 \times 2^{n-k-2}$ for $7\times 2^{k-2}-1\leq n<2^{k+1}-1$, $k>1$. This is an improved upper bound for this range as compared to earlier work. Comment: 10 pages, 1 figure, and 3 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.06671 Zobrazit plný text záznamu View this record from Arxiv