DOI QR코드

DOI QR Code

H-V -SUPER MAGIC DECOMPOSITION OF COMPLETE BIPARTITE GRAPHS

  • Received : 2015.03.18
  • Published : 2015.06.30

Abstract

An H-magic labeling in a H-decomposable graph G is a bijection $f:V(G){\cup}E(G){\rightarrow}\{1,2,{\cdots},p+q\}$ such that for every copy H in the decomposition, $\sum{_{{\upsilon}{\in}V(H)}}\;f(v)+\sum{_{e{\in}E(H)}}\;f(e)$ is constant. f is said to be H-V -super magic if f(V(G))={1,2,...,p}. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are H-V -super magic decomposable where $$H{\sim_=}K_{1,n}$$ with $n{\geq}1$.

Keywords

References

  1. J. Akiyama and M. Kano, Path Factors of a Graph, Graphs and Applications, Wiley, Newyork, 1985.
  2. G. Chartrand and L. Lesniak, Graphs and Digraphs, 3rd Edition, Chapman and Hall, Boca Raton, London, New-York, Washington, D.C., 1996.
  3. G. Chartrand and P. Zhang, Chromatic Graph Theory, Chapman and Hall, CRC, Boca Raton, 2009.
  4. Y. Egawa, M. Urabe, T. Fukuda, and S. Nagoya, A decomposition of complete bipartite graphs into edge-disjoint subgraphs with star components, Discrete Math. 58 (1986), no. 1, 93-95. https://doi.org/10.1016/0012-365X(86)90190-1
  5. H. Emonoto, Anna S Llado, T. Nakamigawa, and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998), 105-109.
  6. J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 16 (2013), #DS6.
  7. A. Gutierrez and A. Llado, Magic coverings, J. Combin. Math. Combin. Comput. 55 (2005), 43-56.
  8. N. Inayah, A. Llado, and J. Moragas, Magic and antimagic H-decompositions, Discrete Math. 312 (2012), no. 7, 1367-1371. https://doi.org/10.1016/j.disc.2011.11.041
  9. T. Kojima, On $C_4$-Supermagic labelings of the Cartesian product of paths and graphs, Discrete Math. 313 (2013), no. 2, 164-173. https://doi.org/10.1016/j.disc.2012.09.005
  10. Z. Liang, Cycle-supermagic decompositions of complete multipartite graphs, Discrete Math. 312 (2012), no. 22, 3342-3348. https://doi.org/10.1016/j.disc.2012.07.033
  11. A. Llado and J. Moragas, Cycle-magic graphs, Discrete Math. 307 (2007), no. 23, 2925-2933. https://doi.org/10.1016/j.disc.2007.03.007
  12. J. A. MacDougall, M. Miller, Slamin, and W. D. Wallis, Vertex-magic total labelings of graphs, Util. Math. 61 (2002), 3-21.
  13. J. A. MacDougall, M. Miller, and K. Sugeng, Super vertex-magic total labeling of graphs, Proc. 15th AWOCA (2004), 222-229.
  14. G. Marimuthu and M. Balakrishnan, E-super vertex magic labelings of graphs, Discrete Appl. Math. 160 (2012), no. 12, 1766-1774. https://doi.org/10.1016/j.dam.2012.03.016
  15. G. Marimuthu and M. Balakrishnan, Super edge magic graceful graphs, Inform. Sci. 287 (2014), 140-151. https://doi.org/10.1016/j.ins.2014.07.027
  16. A. M. Marr and W. D. Wallis, Magic Graphs, 2nd edition, Birkhauser, Boston, Basel, Berlin, 2013.
  17. T. K. Maryati, A. N. M. Salman, E. T. Baskoro, J. Ryan, and M. Miller, On H-Supermagic labeling for certain shackles and amalgamations of a connected graph, Util. Math. 83 (2010), 333-342.
  18. A. A. G. Ngurah, A. N. M. Salman, and L. Susilowati, H-Supermagic labeling of graphs, Discrete Math. 310 (2010), no. 8, 1293-1300. https://doi.org/10.1016/j.disc.2009.12.011
  19. M. Roswitha and E. T. Baskoro, H-Magic covering on some classes of graphs, AIP Conf. Proc. 1450 (2012), 135-138.
  20. J. Sedlacek, Problem 27, Theory of Graphs and its Applications, 163-167, Proceedings of Symposium Smolenice, 1963.
  21. K. A. Sugeng and W. Xie, Construction of Super edge magic total graphs, Proc. 16th AWOCA (2005), 303-310.
  22. T.-M. Wang and G.-H. Zhang, Note on E-super vertex magic graphs, Discrete Appl. Math. 178 (2014), 160-162. https://doi.org/10.1016/j.dam.2014.06.009