On Imbalances in Oriented Tripartite Graphs

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 =...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2011-05, Vol.27 (5), p.927-932
Main Authors: Pirzada, S., Naikoo, T. A., Shah, Nasir A.
Format: Article
Language:English
Subjects:
Criteria
DUS
Graph theory
Graphs
Integers
Mathematical analysis
Mathematics
Mathematics and Statistics
Studies
不平衡
关键词
图形边缘
有向图
用户界面
面向图形
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Summary: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
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-8459-6