Pirzada, A.; Al-Assaf, Abdulaziz M.; Kayibi, Koko K. On imbalances in oriented multipartite graphs. (English) Zbl 1268.05092 Acta Univ. Sapientiae, Math. 3, No. 1, 34-42 (2011). Summary: An oriented \(k\)-partite graph (multipartite graph) is the result of assigning a direction to each edge of a simple \(k\)-partite graph. Let \(D(V_1, V_2, \ldots, V_k)\) be an oriented \(k\)-partite graph, and let \(d^{+}_{v_{ij}}\) and \(d^{-}_{v_{ij}}\) be respectively the outdegree and indegree of a vertex \(v_{ij}\) in \(V_i\). Define \(b_{v_{ij}}\) (or simply \(b_{ij}\) as \(b_{ij} = d^{+}_{v_{ij}}-d^{-}_{v_{ij}}\) as the imbalance of the vertex \(v_{ij}\).In this paper, we characterize the imbalances of oriented \(k\)-partite graphs and give a constructive and existence criteria for sequences of integers to be the imbalances of some oriented \(k\)-partite graph. Also, we show the existence of an oriented \(k\)-partite graph with the given imbalance set. Cited in 1 Document MSC: 05C20 Directed graphs (digraphs), tournaments Keywords:digaph; imbalance; outdegree; indegree; oriented graph; oriented multipartite graph; arc PDFBibTeX XMLCite \textit{A. Pirzada} et al., Acta Univ. Sapientiae, Math. 3, No. 1, 34--42 (2011; Zbl 1268.05092) Full Text: EMIS