Isomorphic Types on Graphs: 1-Neighborhood Random Graphs
Any vertex in a graph can be uniquely numbered (here they are colored) based on its one-neighborhood isomorphic type. A one-neighborhood isomorphic type is a graph isomorphism of the graph on all vertices of distance one from the given vertex with all edges within this vertex set. The first eight isomorphic types are shown in the legend.
This Demonstration shows unique coloring for all vertices with a valency of three or less, and black for all vertices with a valency greater than three.