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 dx^＋ and dx^- denote the outdegree and...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 dx^＋ and dx^- denote the outdegree and indegree respectively of x. Define aui： dui^＋ - dus^-, bvj = dvj^＋ - dvj^- and cwk = dwk^＋ - dwk^- as the imbalances of the vertices ui in U, vj in V and wk in W respectively. In this paper, we obtain criteria for sequences of integers to be the imbalances of some oriented tripartite graph. Keywords Digraph, imbalance, outdegree, indegree, oriented graph, oriented tripartite graph, arc展开更多
文摘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 dx^＋ and dx^- denote the outdegree and indegree respectively of x. Define aui： dui^＋ - dus^-, bvj = dvj^＋ - dvj^- and cwk = dwk^＋ - dwk^- as the imbalances of the vertices ui in U, vj in V and wk in W respectively. In this paper, we obtain criteria for sequences of integers to be the imbalances of some oriented tripartite graph. Keywords Digraph, imbalance, outdegree, indegree, oriented graph, oriented tripartite graph, arc
