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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. 

References

Ahmad, A., López, S. C., Muntaner-Batle, F. A. and Rius-Font, M., ‘Enumerating super edge-magic labeling for the union of nonisomorphic graphs’, Bull. Aust. Math. Soc. 84(2) (2010), 310–321.CrossRefGoogle Scholar
Bacǎ, M., ‘On magic labelings of grid graphs’, Ars Combin. 40 (1990), 295–299.Google Scholar
Bacǎ, M., Bashir, F. and Semaničová-Feňovčíková, A., ‘Face antimagic labelings of antiprisms’, Util. Math. 84 (2011), 209–224.Google Scholar
Bacǎ, M., Nauman, M. and Shabbir, A., ‘Labelings of type (1, 1, 1) for toroidal fullerenes’, Turkish J. Math. 37 (2013), 899–907.Google Scholar
Gallian, J. A., ‘A dynamic survey of graph labeling’, Electron. J. Combin. 17 (2014), #DS6.Google Scholar
Gutierrez, A. and Lladó, A., ‘Magic coverings’, J. Combin. Math. Combin. Comput. 55 (2005), 43–56.Google Scholar
Jeyanthi, P. and Selvagopal, P., ‘Some C 4-super magic graphs’, Ars Combin. 111 (2013), 129–136.Google Scholar
Jeyanthi, P., Selvagopal, P. and Sundaram, S. S., ‘Some C 3-super magic graphs’, Util. Math. 89 (2012), 357–366.Google Scholar
Kotzig, A. and Rosa, A., ‘Magic valuations of finite graphs’, Canad. Math. Bull. 13 (1970), 451–461.CrossRefGoogle Scholar
Lladó, A. and Moragas, J., ‘Cycle-magic graphs’, Discrete Math. 307 (2007), 2925–2933.CrossRefGoogle Scholar
López, S. C., Muntaner-Batle, F. A. and Rius-Font, M., ‘Perfect super edge-magic graphs’, Bull. Math. Soc. Sci. Math. Roumanie 55(103) No 2 (2012), 199–208.Google Scholar
Maryati, T. K., Salman, A. N. M. and Baskoro, E. T., ‘Supermagic coverings of the disjoint union of graphs and amalgamations’, Discrete Math. 313 (2013), 397–405.CrossRefGoogle Scholar
Maryati, T. K., Salman, A. N. M., Baskoro, E. T., Ryan, J. and Miller, M., ‘On H-supermagic labelings for certain shackels and amalgamations of a connected graph’, Util. Math. 83 (2010), 333–342.Google Scholar
Ngurah, A. A. G., Salman, A. N. M. and Susilowati, L., ‘H-supermagic labeling of graphs’, Discrete Math. 310 (2010), 1293–1300.CrossRefGoogle Scholar