Signed degree sequences in signed multipartite graphs (Q2822538)

A signed graph is a graph in which each edge is assigned to a positive or a negative sign. The concept of signed graphs was introduced by \textit{F. Harary} [Mich. Math. J. 2, 143--146 (1954; Zbl 0056.42103)]. The set of distinct signed degrees of the vertices in a signed graph is called its signed degree set.NEWLINENEWLINENEWLINE \textit{D. Hoffman} and \textit{H. Jordan} [J. Graph Theory 52, No. 1, 27--36 (2006; Zbl 1117.05089)] have shown that the degree sequences of signed graphs can be characterized by a system of linear inequalities. The set of all \(n\)-tuples satisfying the system of linear inequalities is a polytope. \textit{S. Pirzada} [J. Comb. Inf. Syst. Sci. 37, No. 2--4, 179--204 (2012; Zbl 1300.05068)] gave necessary and sufficent conditions for two sequences of integers to be the signed degree sequences of some signed bipartite graph. NEWLINENEWLINENEWLINE \textit{S. Pirzada} et al. [Appl. Anal. Discrete Math. 2, No. 1, 114--117 (2008; Zbl 1199.05159)] worked on signed degree sets in bipartite graphs. Also, many results are obtained for signed tripartite graphs in many researches.NEWLINENEWLINEHere, the authors utilize the concept of signed degree set, the signed degree sequences of signed \(k\)-partite graphs and present their existence.