Browse > Article
http://dx.doi.org/10.4134/CKMS.2015.30.3.313

H-V -SUPER MAGIC DECOMPOSITION OF COMPLETE BIPARTITE GRAPHS  

KUMAR, SOLOMON STALIN (Department of Mathematics The American College)
MARIMUTHU, GURUSAMY THEVAR (Department of Mathematics The American College)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.3, 2015 , pp. 313-325 More about this Journal
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
H-decomposable graph; H-V -super magic labeling; complete bipartite graph;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI   ScienceOn
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.   DOI   ScienceOn
9 T. Kojima, On $C_4$-Supermagic labelings of the Cartesian product of paths and graphs, Discrete Math. 313 (2013), no. 2, 164-173.   DOI   ScienceOn
10 Z. Liang, Cycle-supermagic decompositions of complete multipartite graphs, Discrete Math. 312 (2012), no. 22, 3342-3348.   DOI   ScienceOn
11 A. Llado and J. Moragas, Cycle-magic graphs, Discrete Math. 307 (2007), no. 23, 2925-2933.   DOI   ScienceOn
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.   DOI   ScienceOn
15 G. Marimuthu and M. Balakrishnan, Super edge magic graceful graphs, Inform. Sci. 287 (2014), 140-151.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn