The new commands GraphTheory[CanonicalGraph], GraphTheory[Eccentricity], and GraphTheory[Radius] enable the construction of new graph normal forms and the computation of quantities from graphs.
The CanonicalGraph command constructs a version of the input graph in which the vertices have been reordered such that the resulting graph is in a canonical form. The output is canonical in the sense that any two graphs and are isomorphic if and only if . In this example, the Foster cage graph and the Meringer graph serve as examples of graphs which are both cage graphs with the same number of vertices and edges, but are nevertheless not isomorphic.
| (3.1) |
| (3.2) |
The new command Eccentricity computes the eccentricity of the graph at a specified vertex or, if not specified, computes the list of eccentricities at each vertex. The eccentricity of a vertex is the maximum graph distance between and any other vertex in the graph.
| (3.4) |
The maximum eccentricity over the entire graph is known as the graph diameter and can be computed with GraphTheory[Diameter] (also available in previous Maple versions).
The minimum eccentricity over the entire graph is known as the graph radius, and it can be computed directly using the new command Radius: