Mathematics in Computer Science

, Volume 7, Issue 2, pp 245–253

# Super Face Antimagic Labelings of Union of Antiprisms

• Martin Bača
• Muhammad Kamran Siddiqui
Article

## Abstract

In this paper we deal with the problem of labeling the vertices, edges and faces of a disjoint union of m copies of antiprism by the consecutive integers starting from 1 in such a way that the set of face-weights of all s-sided faces forms an arithmetic progression with common difference d, where by the face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face. Such a labeling is called super if the smallest possible labels appear on the vertices. The paper examines the existence of such labelings for union of antiprisms for several values of the difference d.

## Keywords

Plane graph Super d-antimagic labeling Disjoint union of antiprisms

05C78

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## References

1. 1.
Ali G., Bača M., Bashir F., Semaničová-Feňovčíková, A: On face antimagic labelings of disjoint union of prisms. Utilitas Math. 85, 97–112 (2011)
2. 2.
Bača M.: On magic labelings of grid graphs. Ars Combin. 33, 295–299 (1992)
3. 3.
Bača M.: On magic labelings of honeycomb. Discrete Math.105, 305–311 (1992)
4. 4.
Bača M., Bashir F., Semaničová A.: Face antimagic labelings of antiprisms. Utilitas Math.84, 209–224 (2011)
5. 5.
Bača M., Brankovic L., Semaničová-Feňovčíková, A.: Labelings of plane graphs containing Hamilton path. Acta Math. Sin. (Engl. Ser.) 27, 701–714 (2011)
6. 6.
Bača M., Miller M.: On d-antimagic labelings of type (1, 1, 1) for prisms. J. Combin. Math. Combin. Comput. 44, 199–207 (2003)
7. 7.
Bača M., Miller M., Phanalasy O., Semaničová-Feňovčíková, A.: Super d-antimagic labelings of disconnected plane graphs. Acta Math. Sin. (Engl. Ser.) 26, 2283–2294 (2010)
8. 8.
Figueroa-Centeno R.M., Ichishima R., Muntaner-Batle F.A.: The place of super edge-magic labelings among other classes of labelings. Discrete Math. 231, 153–168 (2001)
9. 9.
Figueroa-Centeno R.M., Ichishima R., Muntaner-Batle F.A.: On edge-magic labelings of certain disjoint unions of graphs. Aust. J. Combin. 32, 225–242 (2005)
10. 10.
Kathiresan K., Gokulakrishnan S.: On magic labelings of type (1, 1, 1) for the special classes of plane graphs. Utilitas Math. 63, 25–32 (2003)
11. 11.
Kotzig A., Rosa A.: Magic valuations of finite graphs. Can. Math. Bull. 13, 451–461 (1970)
12. 12.
Lih K.W.: On magic and consecutive labelings of plane graphs. Utilitas Math. 24, 165–197 (1983)
13. 13.
Lin Y., Slamin Bača M., Miller M.: On d-antimagic labelings of prisms. Ars Comin. 72, 65–76 (2004)
14. 14.
Marr A.M., Wallis W.D.: Magic Graphs. Birkhäuser, New York (2013)
15. 15.
Simanjuntak, R., Miller, M., Bertault, F.: Two new (a, d)-antimagic graph labelings. In: Proceedings of Eleventh Australasian Workshop on Combinatorial Algorithms, pp. 179–189 (2000)Google Scholar
16. 16.
Sugeng K.A., Miller M., Lin Y., Bača M.: Face antimagic labelings of prisms. Utilitas Math. 71, 269–286 (2006)
17. 17.
Wallis W.D.: Magic Graphs. Birkhäuser, Boston (2001)

© Springer Basel 2013

• Martin Bača
• 1