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Universal circuit matrix for adjacency graphs of feedback functions

✍ Scribed by Jerzy Żurawiecki

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
267 KB
Volume
126
Category
Article
ISSN
0012-365X

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✦ Synopsis

We define the class of undirected graphs associated with the feedback functions. Next, we construct a mapping which transforms a given feedback function into the circuit matrix of the corresponding graph. This mapping establishes some linear dependences between the nonlinear feedback functions, so it may be a useful tool for the study of such functions.

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Let G be a graph without loops and multiple edges. If V(G) = {vl, v2 .... , v,}, we define the adjacency matrix of G to be the n x n (0, D-matrix A(G) = (aij), where ais = l if viv s e E(G) and ais = 0 otherwise. G is said to be singular if the matrix A(G) is singular. Reduction procedures which wil