Group distance magic and antimagic graphs

S. Cichacz; D. Froncek; K. Sugeng; Sanming Zhou

doi:10.1016/j.endm.2015.05.007

Group distance magic and antimagic graphs

S. Cichacz, D. Froncek, K. Sugeng, Sanming Zhou

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V(G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V(G) to A such that all vertices of G have the same weight. In this paper we study these new labellings with a focus on product graphs.

Original language	English (US)
Pages (from-to)	41-48
Number of pages	8
Journal	Electronic Notes in Discrete Mathematics
Volume	48
DOIs	https://doi.org/10.1016/j.endm.2015.05.007
State	Published - Jul 1 2015

Bibliographical note

Funding Information:
1 Partially supported by the Polish Ministry of Science and Higher Education. 2 Email: cichacz@agh.edu.pl 3 Email: dalibor@d.umn.edu 4 Email: kiki@sci.ui.ac.id 5 Supported by the Australian Research Council. 6 Email: smzhou@ms.unimelb.edu.au

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Distance antimagic labelling
Distance magic labelling
Group labelling

Access

10.1016/j.endm.2015.05.007

OpenUrl availability

Full text

Cite this

@article{8bc575fd8f7f4364b31307c5e4795eb5,

title = "Group distance magic and antimagic graphs",

abstract = "Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V(G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V(G) to A such that all vertices of G have the same weight. In this paper we study these new labellings with a focus on product graphs.",

keywords = "Distance antimagic labelling, Distance magic labelling, Group labelling",

author = "S. Cichacz and D. Froncek and K. Sugeng and Sanming Zhou",

note = "Funding Information: 1 Partially supported by the Polish Ministry of Science and Higher Education. 2 Email: cichacz@agh.edu.pl 3 Email: dalibor@d.umn.edu 4 Email: kiki@sci.ui.ac.id 5 Supported by the Australian Research Council. 6 Email: smzhou@ms.unimelb.edu.au Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2015",

month = jul,

day = "1",

doi = "10.1016/j.endm.2015.05.007",

language = "English (US)",

volume = "48",

pages = "41--48",

journal = "Electronic Notes in Discrete Mathematics",

issn = "1571-0653",

publisher = "Elsevier",

}

TY - JOUR

T1 - Group distance magic and antimagic graphs

AU - Cichacz, S.

AU - Froncek, D.

AU - Sugeng, K.

AU - Zhou, Sanming

N1 - Funding Information: 1 Partially supported by the Polish Ministry of Science and Higher Education. 2 Email: cichacz@agh.edu.pl 3 Email: dalibor@d.umn.edu 4 Email: kiki@sci.ui.ac.id 5 Supported by the Australian Research Council. 6 Email: smzhou@ms.unimelb.edu.au Publisher Copyright: © 2015 Elsevier B.V.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V(G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V(G) to A such that all vertices of G have the same weight. In this paper we study these new labellings with a focus on product graphs.

AB - Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V(G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V(G) to A such that all vertices of G have the same weight. In this paper we study these new labellings with a focus on product graphs.

KW - Distance antimagic labelling

KW - Distance magic labelling

KW - Group labelling

UR - http://www.scopus.com/inward/record.url?scp=84937485220&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937485220&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2015.05.007

DO - 10.1016/j.endm.2015.05.007

M3 - Article

AN - SCOPUS:84937485220

SN - 1571-0653

VL - 48

SP - 41

EP - 48

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Group distance magic and antimagic graphs

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this