DOI QR코드

DOI QR Code

ON CONSTRUCTIONS OF NEW SUPER EDGE-MAGIC GRAPHS FROM SOME OLD ONES BY ATTACHING SOME PENDANTS

  • Received : 2016.03.02
  • Published : 2017.01.31

Abstract

Baskoro et al. [1] provided some constructions of new super edge-magic graphs from some old ones by attaching 1, 2, or 3 pendant vertices and edges. In this paper, we introduce (q, m)-super edge-magic total labeling and we give a construction of new super edge-magic graphs by attaching n pendant vertices and edges under some conditions, for any positive integer n. Also, we give a constraint on our construction.

Keywords

References

  1. E. T. Baskoro, I. W. Sudarsana, and Y. M. Cholily, How to construct new super edgemagic graphs from some old ones, J. Indones. Math. Soc. 11 (2005), no. 2, 155-162.
  2. H. Enomoto, A. Llado, T. Nakamigawa, and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998), no. 2, 105-109.
  3. R. M. Figueroa-Centeno, R. Ichishima, and F. A. Muntaner-Batle, On super edge-magic graphs, Ars Combin. 64 (2002), 81-95.
  4. A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull. 13 (1970), 451-461. https://doi.org/10.4153/CMB-1970-084-1
  5. A. M. Marr and W. D. Wallis, Magic Graphs, Second ed., Birkhauser, Boston, 2012.
  6. I. W. Sudarsana, E. T. Baskoro, D. Ismaimuza, and H. Assiyatun, Creating new super edge-magic total labelings from old ones, J. Combin. Math. Combin. Comput. 55 (2005), 83-90.