Transformations of edge-coloured cubic graphs Original Research Article

For a simple 3-edge-coloured cubic graph, an edge-c-reduction and three transformations (S-, X-, and H-transformation) are defined. Each transformation preserves order and regularity of graphs. They also define metrics on the set of all (connected) 3-edge-coloured cubic graphs with the same order. All connected irreducible 3-edge-coloured cubic graphs are determined.