Software for Discovery in Graph Theory

The Algorithms Lab has been involved since its creation in the development of software tools aimed at helping researchers find new results in graph theory, at all levels of the discovery process: conjectures, proofs and counterexamples.

PHOEG (and GraPHedron)

The first system developed was GraPHedron. It used a geometric approach to help find conjectures in extremal graph theory. It has today been replaced by PHOEG (acronym for “PHOEG Helps Obtaining Extremal Graphs”) which still uses this geometric approach but also offers an interactive web interface to explore the relationships between graph invariants.

PHOEG can be accessed at https://phoeg.umons.ac.be/phoeg.

ChemicHull

ChemicHull is a specific tool that provides a complete polyhedral description of chemical graphs with a maximum degree of at most 3. It allows users to quickly determine which molecular graphs minimize or maximize a given topological index, whatever it may be, even if defined online by the user. It is accessible via https://phoeg.umons.ac.be/chemichull.

House of Graphs

Researchers from the Algorithms Lab are involved in the creation of House of Graphs (initial version and new version). This website used by more than 500 registered users is an open database of interesting graphs.

House of Graphs can be accessed at https://houseofgraphs.org.