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Title

BALANCED DEGREE-MAGIC LABELINGS OF COMPLETE BIPARTITE GRAPHS UNDER BINARY OPERATIONS

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 Start Page 1 | End Page 13

Abstract

 A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E (G) | such that the sum of the labels of the edges incident with any vertex v is equal to (1+|E (G) |) deg (v) /2.Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of COMPLETE BIPARTITE GRAPHS.

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