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Mathematica Bohemica
Article . 2002 . Peer-reviewed
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zbMATH Open
Article . 2002
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Induced-paired domatic numbers of graphs

Authors: Zelinka, Bohdan;

Induced-paired domatic numbers of graphs

Abstract

Summary: A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(D\), or is adjacent to a vertex of \(D\). If moreover the subgraph \(\langle D\rangle\) of \(G\) induced by \(D\) is regular of degree 1, then \(D\) is called an induced-paired dominating set in \(G\). A partition of \(V(G)\), each of whose classes is an induced-paired dominating set in \(G\), is called an induced-paired domatic partition of \(G\). The maximum number of classes of an induced-paired domatic partition of \(G\) is the induced-paired domatic number of \(G\). This paper studies its properties.

Keywords

Extremal problems in graph theory, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), induced-paired domatic number, induced-paired dominating set, dominating set

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Published in a Diamond OA journal