On a problem concerning $k$-subdomination numbers of graphs

Title:

On a problem concerning $k$-subdomination numbers of graphs

Creator:

Zelinka, Bohdan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ec02719a-d6ab-4f35-bfb1-adf2ff936f79
uuid:ec02719a-d6ab-4f35-bfb1-adf2ff936f79

Subject:

$k$-subdomination number of a graph and three-dimensional cube graph

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

One of numerical invariants concerning domination in graphs is the $k$-subdomination number $\gamma ^{-11}_{kS}(G)$ of a graph $G$. A conjecture concerning it was expressed by J. H. Hattingh, namely that for any connected graph $G$ with $n$ vertices and any $k$ with $\frac{1}{2} n < k \leqq n$ the inequality $\gamma ^{-11}_{kS}(G) \leqq 2k - n$ holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and $k=5$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

627-629

Source:

Czechoslovak Mathematical Journal | 2003 Volume:53 | Number:3

Harvested from:

CDK

Metadata only:

false