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Further Results on Complementary Super Edge Magic Graph Labeling

Neelam Kumari1 and Seema Mehra2
Department of Mathematics, M.D. University, Rohtak (Haryana), India
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Abstract

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
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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.
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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,
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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.

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