Evolution Operator of the Bipartite Orbit of Graphs

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.