About non-isomorphic graph colouring generating by Read–Faradzhev method

We consider the problem of generating all the non-isomorphic vertex $k$-colourings of a graph. The main point is to provide an algorithm for solving the problem without isomorphism testing technique proposed in Read–Faradzhev method. The algorithm is based on the backtracking method. Each iteration calculates the set of orbits for a given colouring, selects one representative from each orbit, and each representative is coloured in all colors in a selected way. From the set of colourings thus obtained, not canonical are cut off. The generation proceeds until canonical colourings remain.