Abstract
An oriented tripartite graph is the result of assigning a direction to each edge of a simple tripartite graph. For any vertex x in an oriented tripartite graph D(U,V,W), let d + x and d − x denote the outdegree and indegree respectively of x. Define \( a_{u_i } = d_{u_i }^ + - d_{u_i }^ - , b_{v_j } = d_{v_j }^ + - d_{v_j }^ - \) and \( c_{w_k } = d_{w_k }^ + - d_{w_k }^ - \) as the imbalances of the vertices u i in U, v j in V and w k in W respectively. In this paper, we obtain criteria for sequences of integers to be the imbalances of some oriented tripartite graph.
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The first author is supported by the project IN090044 of King Fahd University of Petroleum and Minerals
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Pirzada, S., Naikoo, T.A. & Shah, N.A. On imbalances in oriented tripartite graphs. Acta. Math. Sin.-English Ser. 27, 927–932 (2011). https://doi.org/10.1007/s10114-011-8459-6
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DOI: https://doi.org/10.1007/s10114-011-8459-6