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ON CYCLE-SUPERMAGICNESS OF SUBDIVIDED GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  05 May 2015

SYED TAHIR RAZA RIZVI ,
MADIHA KHALID ,
KASHIF ALI ,
MIRKA MILLER  and
JOE RYAN
SYED TAHIR RAZA RIZVI*
Affiliation:
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Lahore, Pakistan email strrizvi@gmail.com
MADIHA KHALID
Affiliation:
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Lahore, Pakistan email madihakhalid63@gmail.com
KASHIF ALI
Affiliation:
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Lahore, Pakistan email akashifali@gmail.com
MIRKA MILLER
Affiliation:
School of Mathematical and Physical Sciences, The University of Newcastle, Australia Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic Department of Informatics, King’s College London, UK email mirka.miller@newcastle.edu.au
JOE RYAN
Affiliation:
School of Electrical Engineering and Computer Sciences, The University of Newcastle, Australia email joe.ryan@newcastle.edu.au
*
✉strrizvi@gmail.com
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Abstract

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Lladó and Moragas [‘Cycle-magic graphs’, Discrete Math.307 (2007), 2925–2933] showed the cyclic-magic and cyclic-supermagic behaviour of several classes of connected graphs. They discussed cycle-magic labellings of subdivided wheels and friendship graphs, but there are no further results on cycle-magic labellings of other families of subdivided graphs. In this paper, we find cycle-magic labellings for subdivided graphs. We show that if a graph has a cycle-(super)magic labelling, then its uniform subdivided graph also has a cycle-(super)magic labelling. We also discuss some cycle-supermagic labellings for nonuniform subdivided fans and triangular ladders.

Keywords

cycle-magic graphsubdivided graphs

MSC classification

Primary: 05C78: Graph labelling (graceful graphs, bandwidth, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 11 - 18
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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