GraphTheory
Maple 2018 enhances the GraphTheory package with new functions, including:
CliquePolynomial
DistancePolynomial
FindClique
GraphIntersection
IndependencePolynomial
IsReachable
Reachable
The ChromaticNumber function includes a new heuristic for graph coloring.
The SpecialGraphs subpackage also includes commands for eight new graphs.
Examples
New Special Graphs
FindClique returns a list of vertices which comprise a clique in the graph G. The optional parameter size specifies a size for the clique.
GraphIntersection returns a graph G which is the intersection of the graphs G1,...,Gs, such that
IndependencePolynomial returns the independence polynomial for the graph G in the variable x.
ChromaticNumber
ChromaticNumber returns the minimum number of colours necessary to colour the vertices of a graph so that no adjacent vertices are coloured the same. Maple 2018 includes a new heuristic, method=sat, which transforms the graph into an instance of the Boolean satisfiability problem which it then solves using the Logic[Satisfy] command. The new default heuristic, method=fastest, runs the two methods optimal and sat in parallel and returns the result of whichever method finishes first.
The SpecialGraphs subpackage now includes built-in commands to generate the following special graphs:
Doyle Graph
Gear Graph
Gray Graph
Mirzakhani Graph
Nauru Graph
Poussin Graph
Turan Graph
Tutte Graph
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