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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| Published in | Mathematica Slovaca Vol. 59; no. 1; pp. 1 - 18 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
SP Versita
01.02.2009
Versita |
| Subjects | |
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| ISSN | 0139-9918 1337-2211 1337-2211 |
| DOI | 10.2478/s12175-008-0108-x |
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| Abstract | 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. |
|---|---|
| AbstractList | 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
2n+1 while other stricter labelings yielded cyclic G-decompositions of K
2nx+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. 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. |
| Author | Eynden, Charles Vanden El-Zanati, Saad I. |
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| CitedBy_id | crossref_primary_10_1016_j_disc_2021_112339 crossref_primary_10_1016_j_akcej_2018_11_003 crossref_primary_10_1002_jgt_21632 crossref_primary_10_1007_s00039_017_0416_9 crossref_primary_10_1016_j_disc_2011_09_017 crossref_primary_10_1002_jcd_20226 crossref_primary_10_1007_s40840_017_0503_y crossref_primary_10_3390_math12121879 crossref_primary_10_1016_j_endm_2017_06_003 |
| Cites_doi | 10.1016/0012-365X(93)E0095-L 10.1016/0012-365X(95)00171-R 10.1016/0095-8956(81)90031-9 10.1016/S0012-365X(00)00318-6 10.1002/jcd.20170 10.1016/S0012-365X(00)00233-8 10.1016/j.disc.2003.11.061 10.1016/j.disc.2003.11.024 10.1002/jgt.20024 |
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| Keywords | cyclic graph decomposition graph valuation graph labeling Rosa-type labeling Secondary 05-02 Primary 05C78 |
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| References | Poljak, Sûra (CR34) 1982; 14 Huang, Rosa (CR31) 1978; 5 West (CR38) 1996 Dinitz, Rodney (CR17) 1997; 52 Huang, Kotzig, Rosa (CR30) 1982; 21 CR19 Hrnčiar, Haviar (CR29) 2001; 233 Abrham, Kotzig (CR2) 1996; 150 Aldred, Mckay (CR7) 1998; 23 CR16 El-Zanati, Kenig, Vanden Eynden (CR21) 2000; 21 Blinco, El-Zanati, Vanden Eynden (CR10) 2004; 284 CR15 CR14 CR36 Kotzig (CR32) 1981; 31 Aguado, El-Zanati (CR5) 2008; 64 Aguado, El-Zanati, Hake, Stob, Yayla (CR6) 2007; 37 CR12 Abrham, Kotzig (CR1) 1994; 135 Froncek (CR23) 2007; 307 Grannell, Griggs, Holroyd (CR26) 2001; 231 Ringel, Fiedler (CR35) 1964 Adams, Bryant, Buchanan (CR4) 2008; 16 Bosák (CR11) 1990 Rosa, Rosenstiehl (CR37) 1967 CR3 Blinco, El-Zanati (CR9) 2004; 40 El-Zanati, Vanden Eynden, Punnim (CR20) 2001; 24 CR8 CR24 CR22 Lladó, López (CR33) 2005; 48 Golomb, Read (CR25) 1972 Häggkvist (CR27) 1989; 141 Bryant, El-Zanati, Colbourn, Dinitz (CR13) 2007 Edwards, Howard (CR18) 2006; 1 Hevia, Ruiz (CR28) 1987; 9 |
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| Snippet | 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... 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... |
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| SubjectTerms | Algebra cyclic graph decomposition graph labeling graph valuation Mathematics Mathematics and Statistics Primary 05C78 Rosa-type labeling Secondary 05-02 |
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| Title | On Rosa-type labelings and cyclic graph decompositions |
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