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 }^ -
$
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 }^ -
$
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. |