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Opuscula Mathematica
Article . 2006
Data sources: DOAJ
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Equitable coloring of graph products

Authors: Hanna Furmańczyk;

Equitable coloring of graph products

Abstract

A graph is equitably \(k\)-colorable if its vertices can be partitioned into \(k\) independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest \(k\) for which such a coloring exists is known as the equitable chromatic number of \(G\) and denoted by \(\chi_{=}(G)\). It is interesting to note that if a graph \(G\) is equitably \(k\)-colorable, it does not imply that it is equitably \((k+1)\)-colorable. The smallest integer \(k\) for which \(G\) is equitably \(k'\)-colorable for all \(k'\geq k\) is called the equitable chromatic threshold of \(G\) and denoted by \(\chi_{=}^{*}(G)\). In the paper we establish the equitable chromatic number and the equitable chromatic threshold for certain products of some highly-structured graphs. We extend the results from [Chen B.-L., Lih K.-W., Yan J.-H., Equitable coloring of graph products, manuscript, 1998] for Cartesian, weak and strong tensor products.

Keywords

equitable coloring, T57-57.97, Applied mathematics. Quantitative methods, graph product

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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!
0
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Published in a Diamond OA journal