Well, that's not the definition we used for color isomorphism. What we do is that in the mapping of the vertices, vertex 'v' can only be mapped to vertex 'w' if they have the same color. My understanding is that this is the "common" definition of isomorphism between colored graphs, but I might be wrong.
Gabor On Wed, Sep 12, 2012 at 9:22 AM, Louis Aslett <[email protected]> wrote: > I might have misunderstood coloured graph isomorphisms, but from my > understanding the following two graphs should be isomorphic (code in > R). > > g1 <- graph.formula(1 -- 2:3, 2 -- 3, 3 -- 4) > g2 <- graph.formula(1 -- 2, 2 -- 3, 2:3 -- 4) > graph.count.isomorphisms.vf2(g1, g2, vertex.color1=c(1,2,2,1), > vertex.color2=c(1,2,2,1)) > > My understanding of coloured isomorphism is that two bijections are > looked for f and g, say, such that f applied to one colour or vertex > and g to the other results in equivalent adjacency to the original > graph. In this case, bijection f which switches 1 and 4, and another > g which switches 2 and 3 does the job (I think). However, the > function says there are no isomorphisms. > > Any thoughts (or corrections to my understanding of coloured > isomorphism) appreciated! > > Louis > > _______________________________________________ > igraph-help mailing list > [email protected] > https://lists.nongnu.org/mailman/listinfo/igraph-help -- Gabor Csardi <[email protected]> MTA KFKI RMKI _______________________________________________ igraph-help mailing list [email protected] https://lists.nongnu.org/mailman/listinfo/igraph-help
