On a problem concerning k-subdomination numbers of graphs.

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F03%3A00000027" target="_blank" >RIV/46747885:24510/03:00000027 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On a problem concerning k-subdomination numbers of graphs.

Original language 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 $frac12 n < k leqq n$ the inequality $gamma^{-11}_{kS}(G) leqq2k - n$ holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and $k=5$.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2003

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Czech. Math. J.

ISSN

0011-4642

e-ISSN

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Volume of the periodical

58

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

4

Pages from-to

621-624

UT code for WoS article

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EID of the result in the Scopus database

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