Signed degree sequences in signed multipartite graphs
S. Pirzada · Hacettepe Journal of Mathematics and Statistics · 2015
A signed k -partite graph (signed multipartite graph) is a k -partite graph in which each edge is assigned a positive or a negative sign. If G ( V 1 , V 2 , · · · , V k ) is a signed k -partite graph with V i = { v i 1 ,v i 2 , ··· ,v in i } , 1 ≤ i ≤ k , the signed degree of v ij is sdeg ( v ij ) = d ij = d + ij − d − ij , where 1 ≤ i ≤ k , 1 ≤ j ≤ n i and d + ij ( d − ij ) is the number of positive (negative) edges incident with v ij . The sequences α i = [ d i 1 ,d i 2 , ··· ,d in i ] , 1 ≤ i ≤ k , are called the signed degree sequences of G ( V 1 ,V 2 , ··· ,V k ) . The set of distinct signed degrees of the vertices in a signed k -partite graph G ( V 1 , V 2 , · · · , V k ) is called its signed degree set. In this paper, we characterize signed degree sequences of signed k -partite graphs. Also, we give the existence of signed k -partite graphs with given signed degree sets.