The Coates graph Gc(A) associated with an n × nmatrixA 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.
^Thulasiraman, K.; Swamy, M. N. S. (1992). "§6.11 The Coates and Mason graphs". Graphs:Theory and Algorithms. John Wiley & Sons. pp. 163–169. ISBN0-471-51356-3.
^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.
April 11, 2024
coates, graph, mathematics, coates, flow, graph, named, after, coates, graph, associated, with, coates, method, solution, system, linear, equations, associated, with, matrix, node, weighted, labeled, directed, graph, nodes, labeled, through, each, associated, . 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 editFlow graph mathematics Mason graphReferences edit Thulasiraman K Swamy M N S 1992 6 11 The Coates and Mason graphs Graphs Theory and Algorithms John Wiley amp 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 Retrieved from https en wikipedia org w index php title Coates graph amp oldid 1168532346, wikipedia, wiki, book, books, library,
