Isomorphic Types on Graphs: 1-Neighborhood Random Tree 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 vertices with a valency greater than three.

External Links

Graph Isomorphism (Wolfram MathWorld)
Local Graph (Wolfram MathWorld)
Tree (Wolfram MathWorld)
Grid Graph (Wolfram MathWorld)
Random Graph (Wolfram MathWorld)

Permanent Citation

John Cicilio
​
​"Isomorphic Types on Graphs: 1-Neighborhood Random Tree Graphs"​
​http://demonstrations.wolfram.com/IsomorphicTypesOnGraphs1NeighborhoodRandomTreeGraphs/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011