• 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}
}
• Published 2012
• Mathematics
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…
5 Citations
#A13 INTEGERS 21A (2021) SPANNING TREES AND DOMINATION IN HYPERCUBES
Let L(G) denote the maximum number of leaves in any spanning tree of a connected graph G. We show the (known) result that for the n-cube Qn, L(Qn) ∼ 2 = |V (Qn)| as n → ∞. Examining this more
The domination number of exchanged hypercubes
• Computer Science
Inf. Process. Lett.
• 2014
Spanning Trees and Domination in Hypercubes.
Let $L(G)$ denote the maximum number of leaves in any spanning tree of a connected graph $G$. We show the (known) result that for the $n$-cube $Q_n$, $L(Q_n) \sim 2^n = |V(Q_n)|$ as \$n\rightarrow
Genetic Approach To Hypercube Problems
The thesis describes the graph-theory problems related to hypercubes such as searching for detour spanners, minimizing their maximal degree and finding multiple edge-disjoint spanners and proposes a solution using a genetic algorithm.
Improved Upper Bound on Independent Domination Number for Hypercubes
• Computer Science, Mathematics
• 2022
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

## References

SHOWING 1-10 OF 18 REFERENCES
Independent perfect domination sets in Cayley graphs
In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that
Improved sphere bounds on the coveting radius of codes
• G. Wee
• Computer Science, Mathematics
IEEE Trans. Inf. Theory
• 1988
The sphere bound is a trivial lower bound on K(n,R), the minimal cardinality of any binary code of length n and with covering radius R. By simple arguments it is considerably improved, to
Introduction to Graph Theory
1. Fundamental Concepts. What Is a Graph? Paths, Cycles, and Trails. Vertex Degrees and Counting. Directed Graphs. 2. Trees and Distance. Basic Properties. Spanning Trees and Enumeration.
From error-correcting codes through sphere packings to simple groups
1. The origin of error-correcting codes an introduction to coding the work of Hamming the Hamming-Holbrook patent the Hamming codes are linear the work of Golay the priority controversy 2. From
Another characterization of hypercubes
• Mathematics
Discret. Math.
• 1982
Independent perfect domination sets in Cayley graphs
In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that ...
Algebraic coding theory
• E. Berlekamp
• Computer Science
McGraw-Hill series in systems science
• 1968
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering