L(2,1)-Labeling of the Strong Product of Paths and Cycles
An L(2,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least two and the labels on vertices at distance two differ by at least one. The span of f is the difference between the largest an...
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| Format: | Article |
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Hindawi Limited
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/741932 |
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doaj-daf48621c4d34367ad4e6e51cf8ef8322020-11-25T00:55:54ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/741932741932L(2,1)-Labeling of the Strong Product of Paths and CyclesZehui Shao0Aleksander Vesel1School of Information Science and Technology, Chengdu University, Chengdu 610106, ChinaFaculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, SloveniaAn L(2,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least two and the labels on vertices at distance two differ by at least one. The span of f is the difference between the largest and the smallest numbers in f(V). The λ-number of G, denoted by λ(G), is the minimum span over all L(2,1)-labelings of G. We consider the λ-number of Pn⊠Cm and for n≤11 the λ-number of Cn⊠Cm. We determine λ-numbers of graphs of interest with the exception of a finite number of graphs and we improve the bounds on the λ-number of Cn⊠Cm, m≥24 and n≥26.http://dx.doi.org/10.1155/2014/741932 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zehui Shao Aleksander Vesel |
| spellingShingle |
Zehui Shao Aleksander Vesel L(2,1)-Labeling of the Strong Product of Paths and Cycles The Scientific World Journal |
| author_facet |
Zehui Shao Aleksander Vesel |
| author_sort |
Zehui Shao |
| title |
L(2,1)-Labeling of the Strong Product of Paths and Cycles |
| title_short |
L(2,1)-Labeling of the Strong Product of Paths and Cycles |
| title_full |
L(2,1)-Labeling of the Strong Product of Paths and Cycles |
| title_fullStr |
L(2,1)-Labeling of the Strong Product of Paths and Cycles |
| title_full_unstemmed |
L(2,1)-Labeling of the Strong Product of Paths and Cycles |
| title_sort |
l(2,1)-labeling of the strong product of paths and cycles |
| publisher |
Hindawi Limited |
| series |
The Scientific World Journal |
| issn |
2356-6140 1537-744X |
| publishDate |
2014-01-01 |
| description |
An L(2,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least two and the labels on vertices at distance two differ by at least one. The span of f is the difference between the largest and the smallest numbers in f(V). The λ-number of G, denoted by λ(G), is the minimum span over all L(2,1)-labelings of G. We consider the λ-number of Pn⊠Cm and for n≤11 the λ-number of Cn⊠Cm. We determine λ-numbers of graphs of interest with the exception of a finite number of graphs and we improve the bounds on the λ-number of Cn⊠Cm, m≥24 and n≥26. |
| url |
http://dx.doi.org/10.1155/2014/741932 |
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AT zehuishao l21labelingofthestrongproductofpathsandcycles AT aleksandervesel l21labelingofthestrongproductofpathsandcycles |
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