On Rosa-type labelings and cyclic graph decompositions

A labeling (or valuation) of a graph G is an assignment of integers to the vertices of G subject to certain conditions. A hierarchy of graph labelings was introduced by Rosa in the late 1960s. Rosa showed that certain basic labelings of a graph G with n edges yielded cyclic G -decompositions of K 2...

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Bibliographic Details
Published inMathematica Slovaca Vol. 59; no. 1; pp. 1 - 18
Main Authors El-Zanati, Saad I., Eynden, Charles Vanden
Format Journal Article
LanguageEnglish
Published Heidelberg SP Versita 01.02.2009
Versita
Subjects
Algebra
cyclic graph decomposition
graph labeling
graph valuation
Mathematics
Mathematics and Statistics
Primary 05C78
Rosa-type labeling
Secondary 05-02
cyclic graph decomposition
graph valuation
graph labeling
Rosa-type labeling
Secondary 05-02
Primary 05C78
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ISSN0139-9918
1337-2211
1337-2211
DOI10.2478/s12175-008-0108-x

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Summary:A labeling (or valuation) of a graph G is an assignment of integers to the vertices of G subject to certain conditions. A hierarchy of graph labelings was introduced by Rosa in the late 1960s. Rosa showed that certain basic labelings of a graph G with n edges yielded cyclic G -decompositions of K 2 n +1 while other stricter labelings yielded cyclic G -decompositions of K 2 nx +1 for all natural numbers x . Rosa-type labelings are labelings with applications to cyclic graph decompositions. We survey various Rosa-type labelings and summarize some of the related results.
ISSN:0139-9918
1337-2211
1337-2211
DOI:10.2478/s12175-008-0108-x