In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations. [1] [2]
The Coates graph Gc(A) associated with an n × n matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry aji ≠ 0 then there is a directed edge from node i to node j with weight aji. [3] In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.
See also
References
- ^ Thulasiraman, K.; Swamy, M. N. S. (1992). "§6.11 The Coates and Mason graphs". Graphs:Theory and Algorithms. John Wiley & Sons. pp. 163–169. ISBN 0-471-51356-3.
- ^ Coates, C.L. (1959). "Flow-graph solutions of linear algebraic equations". IRE Trans. Circuit Theory. CT-6 (2): 170–187. doi: 10.1109/TCT.1959.1086537.
- ^ Wai-Kai Chen (1976). "The associated Coates graph". Applied Graph Theory. North Holland Publishing Company. p. 142.
In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations. [1] [2]
The Coates graph Gc(A) associated with an n × n matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry aji ≠ 0 then there is a directed edge from node i to node j with weight aji. [3] In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.
See also
References
- ^ Thulasiraman, K.; Swamy, M. N. S. (1992). "§6.11 The Coates and Mason graphs". Graphs:Theory and Algorithms. John Wiley & Sons. pp. 163–169. ISBN 0-471-51356-3.
- ^ Coates, C.L. (1959). "Flow-graph solutions of linear algebraic equations". IRE Trans. Circuit Theory. CT-6 (2): 170–187. doi: 10.1109/TCT.1959.1086537.
- ^ Wai-Kai Chen (1976). "The associated Coates graph". Applied Graph Theory. North Holland Publishing Company. p. 142.