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Neelam Kumari Department of Mathematics, M.D. University, Rohtak (Haryana), India^{1} and Seema Mehra^{2} |

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In this paper we introduced the concept of complementary super edge magic labeling and Complementary Super Edge Magic strength of a graph G.A graph G (V, E ) is said to be complementary super edge magic if there exist a bijection f:V U E → { 1, 2, …………p+q } such that p+q+1 - f(x) is constant. Such a labeling is called complementary super edge magic labeling with complementary super edge magic strength. In this paper for a graph G(V, E ) the complementary super edge magic labeling and minimum of all constants which is called complementary super edge magic strength of G is defined. In this paper, we investigate whether some families of graphs are complementary or not?

## Keywords |

Graph Labeling, Edge Magic Labeling ,Total Edge Magic Labeling, Super Edge Magic Labeling, Complementary Super Edge Magic Labeling . |

## INTRODUCTION |

A labeling of a graph G is an assignment of mathematical objects to vertices , edges, or both vertices and edges subject to certain conditions. Graph labeling have applications in coding theory, networking addressing, and in many other fields. In most applications the labels are positive ( or nonnegative ) integers .In 1963 , Sedlack introduced a new class of labeling called magic labeling for a graph G (V, E ) , which is defined as a bijection f from E to a set of positive integers such that |

## MAIN RESULTS |

In this paper the complementary super edge magic labeling and csems of two well known graphs such as the generalized prism Cm × Pn and G T ( n, n, n-1, n, 2n-1) are obtained. Before giving our main results we give a necessary and sufficient conditions for some graphs to have complementary super edge magic labeling. |

Thus f is a super edge-magic of G with constant 15n, G and complementary super edge-magic labeling f is defined as for odd j, |

Thus f (G) is complementary super edge -magic labeling of f with magic constant 21n-6 i.e. csems =21n-6. With this paper, we hope that interest in super edge-magic. and complementary super edgemagic labeling will aroused among those who study graph labeling. |

## References |

[1] D. Craft and E. H Tesar On a question by Erdos about edge magic graph.Discrete Math. 207(1999)271-276 [2] G. Chartrand and L. Lesniak, Graphs and Digraphs,Wadsworth and Books/cole, Advanced Books and software Monterey , C.A(1986) [3] H. Enomoto, A Llado, T. Nakamigawa and G. Ringel, Super edge magic graphs SUT J. Math. 34(1998) [4] R.M Figueroa – Centeno, R. Ichishima and F. A Muntaner Batle, Enlarging the classes of edge magic 2 regular graphs, (pre-print) [5] R. M. Figueroa Centeno, R Ichishima and F. A Muntaner- Batle, On edge magic labeling of certain disjoint unions of graphs, (pre-print) [6] J. A Gallian, A dynamic survey of graph labeling, Electron J. Comb. S (2002) #D56 [7] R. D Godbold and P. Stater, All cycle are edge magic Bull Inst. Combin. Appl. 22(1998)93-97 [8] N.Harts field and G. Ringel, Pearls in Graph Theory, A comprehensive Introduction, Academic Press, San Diego, (1994) [9] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad Math. Bull. 13(1970)451-461 [10] A. Kotzig and A. Rosa, Magic valuations of complete graphs, Publications du Centre de Recherches Mathematiques Universite de Montreal, 175(19 72) [11] G. Ringel and A Llado, Another tree conjecture, Bull. Inst. Combin. Appl. 18(1996)83-85 [12] W. D Wallis, Magic Graphs, Birkhauser Boston (2001) [13] J.A.Gallian, Graph Labeling, Electron. J.Combin. 5(1998)(dynamic survey DS6 [14]R.M. Figueroa-Centeno, R.Ichishima, The place of super edge-magic labeling among other classes of labeling, Discrete Mathematics 231 (2001)153-168 [15] S. Roy and D.G. Akka, On Complementary edge magic of certain graphs, American Journal of Mathematics and Statistics 2012,2(3): 22-66. [16] M.Baca, M.Murugan, Super edge- antimagic labeling of a cycle with a chord , Austral. J. Combin. 35 (2006), 253-261 [17] W. D Wallis, Magic Graphs, Birkhauser, Boston – Basel – Berlin, 2001. [18] K.A.Sugeng, M.Miller and M. Baca , Super edge – antimagic total labeling s , Utilitas Math. 71 (2006), 131-141. [19] Y. Roditty and T. Bachar , A note on edge magic cycles , Bull. Inst. Combin Appl. 29 (2000) , 94- 96. [20] A. Semanicova , Graph Labelig , Ph. D. Thesis , P. J. Safarik University in Kosice , 2006. [21] J.Ivanco , Z. Lastivkova and A. Semanicova, On magic and supermagic line graphs , Math. Bohemica 129 (2004), 33 – 42. [22] R.M. Figueroa-Centeno, R.Ichishima, and F. A. Muntaner – Batle , On super edge magic graphs , Ars Combin. 64 (2002), 81-95 [23] E.T . Baskoro and A.A.G. Ngurah , On super edge magic total labeling of nP3 , Bull. Inst. Combin . Appl. 37 (2003), 82-87. |