Evolution Operator of the Bipartite Orbit of Graphs
Eduardo A. Montenegro *
Department of Mathematics and Statistics, Universidad de Playa Ancha, Lab(e)saM, Laboratorio (experimental) de saberes Matematicos, Valparaso, Chile.
Eduardo M. Cabrera A
Department of Mathematics and Statistics, Universidad de Playa Ancha, Lab(e)saM, Laboratorio (experimental) de saberes Matematicos, Valparaso, Chile.
Jose A. Gonzalez C
Department of Mathematics and Statistics, Universidad de Playa Ancha, Lab(e)saM, Laboratorio (experimental) de saberes Matematicos, Valparaso, Chile.
Ronald A. Manrquez P
Department of Mathematics and Statistics, Universidad de Playa Ancha, Lab(e)saM, Laboratorio (experimental) de saberes Matematicos, Valparaso, Chile.
*Author to whom correspondence should be addressed.
Abstract
The operation of substitution consists of replacing a vertex of a graph by another graph. This new graph is characterized through a function (of substitution) that can be self-definable. The purpose of this work is to construct evolution operators for orbit {wk(G)}, where each element of {wk(G)} is obtained by substituting each vertex of the previous element by a graph. Here, both the initial graph G as the family of graphs of substitution, are known. In this paper, simple and finite graphs will be used, framed in the graphs theory’s area.
Keywords: Graph, distribution operator, substitution of graph, realizable graph, discrete dynamical systems.