Maximal Cliques as a Normal Form in the Algebra of Graphs: Compression by Modular Decomposition and an Enumeration Algorithm
The finite simple graphs with vertices in a set S form an algebra G(S) under union and join, generated by the one-vertex graphs. We show that this algebra has a canonical normal form whose data are exactly the maximal cliques of the graph. Precisely, every g∈G(S) admits a unique maximal-clique decomposition μ(g), chara...