On λ-fold Rosa-type Labelings of Bipartite Multigraphs

© 2017 Elsevier B.V. It is known that for a given (simple) graph G with n edges, there exits a cyclic G-decomposition of K 2n+1 if and only if G admits a ρ-labeling. It is also known that if G is bipartite and it admits an ordered ρ-labeling, then there exists a cyclic G-decomposition of K 2nx+1 f...

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Main Authors: R. C. Bunge, S. I. El-Zanati, J. Mudrock, C. Vanden Eynden, W. Wannasit
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Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/46999
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-469992018-04-25T07:23:07Z On λ-fold Rosa-type Labelings of Bipartite Multigraphs R. C. Bunge S. I. El-Zanati J. Mudrock C. Vanden Eynden W. Wannasit Agricultural and Biological Sciences © 2017 Elsevier B.V. It is known that for a given (simple) graph G with n edges, there exits a cyclic G-decomposition of K 2n+1 if and only if G admits a ρ-labeling. It is also known that if G is bipartite and it admits an ordered ρ-labeling, then there exists a cyclic G-decomposition of K 2nx+1 for every positive integer x. We extend these concepts to labelings of multigraphs through what we call λ-fold ρ-labelings and ordered λ-fold ρ-labelings. Let Kmλ denote the λ-fold complete graph of order m. We sho that if a subgraph G of K2n/λ+1λ has size n, there exits a cyclic G-decomposition of K2n/λ+1λ if and only if G admits a λ-fold ρ-labeling. If in addition G is bipartite and it admits an ordered λ-fold ρ-labeling, then there exists a cyclic G-decomposition of K2nx/λ+1λ for every positive integer x. We discuss some classes of graphs and multigraphs that admit such labelings. 2018-04-25T07:08:46Z 2018-04-25T07:08:46Z 2017-07-01 Journal 15710653 2-s2.0-85021397534 10.1016/j.endm.2017.06.003 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85021397534&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/46999
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Agricultural and Biological Sciences
spellingShingle Agricultural and Biological Sciences
R. C. Bunge
S. I. El-Zanati
J. Mudrock
C. Vanden Eynden
W. Wannasit
On λ-fold Rosa-type Labelings of Bipartite Multigraphs
description © 2017 Elsevier B.V. It is known that for a given (simple) graph G with n edges, there exits a cyclic G-decomposition of K 2n+1 if and only if G admits a ρ-labeling. It is also known that if G is bipartite and it admits an ordered ρ-labeling, then there exists a cyclic G-decomposition of K 2nx+1 for every positive integer x. We extend these concepts to labelings of multigraphs through what we call λ-fold ρ-labelings and ordered λ-fold ρ-labelings. Let Kmλ denote the λ-fold complete graph of order m. We sho that if a subgraph G of K2n/λ+1λ has size n, there exits a cyclic G-decomposition of K2n/λ+1λ if and only if G admits a λ-fold ρ-labeling. If in addition G is bipartite and it admits an ordered λ-fold ρ-labeling, then there exists a cyclic G-decomposition of K2nx/λ+1λ for every positive integer x. We discuss some classes of graphs and multigraphs that admit such labelings.
format Journal
author R. C. Bunge
S. I. El-Zanati
J. Mudrock
C. Vanden Eynden
W. Wannasit
author_facet R. C. Bunge
S. I. El-Zanati
J. Mudrock
C. Vanden Eynden
W. Wannasit
author_sort R. C. Bunge
title On λ-fold Rosa-type Labelings of Bipartite Multigraphs
title_short On λ-fold Rosa-type Labelings of Bipartite Multigraphs
title_full On λ-fold Rosa-type Labelings of Bipartite Multigraphs
title_fullStr On λ-fold Rosa-type Labelings of Bipartite Multigraphs
title_full_unstemmed On λ-fold Rosa-type Labelings of Bipartite Multigraphs
title_sort on λ-fold rosa-type labelings of bipartite multigraphs
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85021397534&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/46999
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