This code contains a formal description of basic facts about Graph Theory and Domination Theory in the language Coq/Ssreflect. It is called DomTheory and consists of: *) The proof that the sum of degrees equals the cardinal of the edge set. *) Definitions and results about open and closed neighborhoods, stable sets, dominating sets, irredundant sets, hereditary and superhereditary properties, maximal/minimal sets and sets of maximum/minimum weight. *) The (weighted version of the) Cockayne-Hedetniemi domination chain. *) Examples of proofs with domination parameters on complete graphs. This code also contains: *) A browsable version made with the tool CoqDocJS, with some ''pretty-print'' symbols (like empty set, summation and set comprehension) added later. *) A solver that computes the (unweighted and weighted versions of) parameters gamma, ii, alpha, Gamma and IR. *) (experimental) The solver also generates a Coq file with a proof of alpha(G) >= k, where k is the size of the best stable set found during the optimization. *) A set of instances.
