Journal of Applied Mathematics

On Super (a,d)-Edge-Antimagic Total Labeling of Special Types of Crown Graphs

Himayat Ullah, Gohar Ali, Murtaza Ali, and Andrea Semaničová-Feňovčíková

Full-text: Open access

Abstract

For a graph G=(V,E), a bijection f from V(G)E(G){1,2,,|V(G)|+|E(G)|} is called (a,d)-edge-antimagic total ((a,d)-EAT) labeling of G if the edge-weights w(xy)=f(x)+f(y)+f(xy),xyE(G), form an arithmetic progression starting from a and having a common difference d, where a>0 and d0 are two fixed integers. An (a,d)-EAT labeling is called super (a,d)-EAT labeling if the vertices are labeled with the smallest possible numbers; that is, f(V)={1,2,,|V(G)|}. In this paper, we study super (a,d)-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 896815, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808051

Digital Object Identifier
doi:10.1155/2013/896815

Mathematical Reviews number (MathSciNet)
MR3074334

Zentralblatt MATH identifier
1271.05087

Citation

Ullah, Himayat; Ali, Gohar; Ali, Murtaza; Semaničová-Feňovčíková, Andrea. On Super $\left(a,d\right)$ -Edge-Antimagic Total Labeling of Special Types of Crown Graphs. J. Appl. Math. 2013 (2013), Article ID 896815, 6 pages. doi:10.1155/2013/896815. https://projecteuclid.org/euclid.jam/1394808051


Export citation

References

  • W. D. Wallis, Magic Graphs, Birkhäuser, Boston, Mass, USA, 2001.
  • D. B. West, An Introduction to Graph Theory, Prentice Hall, 1996.
  • M. Bača and M. Miller, Super Edge-Antimagic Graphs: A Wealth of Problems and Some Solutions, Brown Walker Press, Boca Raton, Fla, USA, 2008.
  • J. A. Gallian, “Dynamic survey of graph labeling,” The Electronic Journal of Combinatorics, vol. 18, 2011.
  • H. Enomoto, A. S. Lladó, T. Nakamigawa, and G. Ringel, “Super edge-magic graphs,” SUT Journal of Mathematics, vol. 34, no. 2, pp. 105–109, 1998.
  • R. M. Figueroa-Centeno, R. Ichishima, and F. A. Muntaner-Batle, “The place of super edge-magic labelings among other classes of labelings,” Discrete Mathematics, vol. 231, no. 1–3, pp. 153–168, 2001.
  • A. Kotzig and A. Rosa, “Magic valuations of finite graphs,” Canadian Mathematical Bulletin, vol. 13, pp. 451–461, 1970.
  • A. Kotzig and A. Rosa, Magic Valuations of Complete Graphs, CRM Publisher, 1972.
  • R. Simanjuntak, F. Bertault, and M. Miller, “Two new (a, d)-antimagic graph labelings,” in Proceedings of the 11th Australasian Workshop on Combinatorial Algorithms, pp. 179–189, 2000.
  • R. Bodendiek and G. Walther, “Arithmetisch antimagische graphen,” in Graphentheorie III, K. Wagner and R. Bodendiek, Eds., BI-Wiss, Mannheim, Germany, 1993.
  • N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, Boston, Mass, USA, 1990.
  • M. Bača, Y. Lin, M. Miller, and R. Simanjuntak, “New constructions of magic and antimagic graph labelings,” Utilitas Mathematica, vol. 60, pp. 229–239, 2001.
  • K. A. Sugeng, M. Miller, Slamin, and M. Bača, “$(a,d)$-edge-antimagic total labelings of caterpillars,” in Combinatorial Geometry and Graph Theory, vol. 3330, pp. 169–180, Springer, Berlin, Germany, 2005.
  • D. R. Silaban and K. A. Sugeng, “Edge antimagic total labeling on paths and unicycles,” Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 65, pp. 127–132, 2008.
  • R. M. Figueroa-Centeno, R. Ichishima, and F. A. Muntaner-Batle, “Magical coronations of graphs,” The Australasian Journal of Combinatorics, vol. 26, pp. 199–208, 2002.
  • M. Bača, Y. Lin, and A. Semaničová, “Note on super antimagicness of disconnected graphs,” AKCE International Journal of Graphs and Combinatorics, vol. 6, no. 1, pp. 47–55, 2009.
  • R. M. Figueroa-Centeno, R. Ichishima, and F. A. Muntaner-Batle, “On edge-magic labelings of certain disjoint unions of graphs,” The Australasian Journal of Combinatorics, vol. 32, pp. 225–242, 2005.
  • M. Bača, F. A. Muntaner-Batle, A. Semaničová-Fenovčíková, and M. K. Shafiq, “On super $(a, 2)$-edge-antimagic total labeling of disconnected čommentComment on ref. [5?]: Please update the information of this reference, if possible.graphs,” Ars Combinatoria. In press.
  • M. Bača, Dafik, M. Miller, and J. Ryan, “Antimagic labeling of disjoint union of $s$-crowns,” Utilitas Mathematica, vol. 79, pp. 193–205, 2009.