Abstract

If each edge of a 3-partite graph is assigned a positive or a negative sign then it is called a signed 3-partite graph. Also, signed degree of a vertex x in a signed 3-partite graph is the number of positive edges incident with x less than the number of negative edges incident with x. The set of distinct signed degrees of the vertices of a signed 3-partite graph is called its signed degree set. In this paper, we prove that every set of n integers is the signed degree set of some connected signed 3-partite graph.

Keywords: Signed graph, signed tripartite graph, signed degree, signed set.

MSC: 05C22

Pages:  121$-$124     

Volume  59 ,  Issue  3 ,  2007