Note on group distance magic complete bipartite graphs

作者：Cichacz Sylwia^*

来源：Central European Journal of Mathematics, 2014, 12(3): 529-533.

DOI：10.2478/s11533-013-0356-z

• Graph labeling
• Abelian group

A I"-distance magic labeling of a graph G = (V, E) with |V| = n is a bijection a"" from V to an Abelian group I" of order n such that the weight of every vertex x a V is equal to the same element A mu a I", called the magic constant. A graph G is called a group distance magic graph if there exists a I"-distance magic labeling for every Abelian group I" of order |V(G)|.
In this paper we give necessary and sufficient conditions for complete k-partite graphs of odd order p to be a"currency sign (p) -distance magic. Moreover we show that if p a parts per thousand 2 (mod 4) and k is even, then there does not exist a group I" of order p such that there exists a I"-distance labeling for a k-partite complete graph of order p. We also prove that K (m,n) is a group distance magic graph if and only if n + m a parts per thousand cent 2 (mod 4).

• 出版日期2014-3