Thanks, yes that's what I meant in my rather imperfect rambling definition! In the example I sent in the first mail, nodes 1 and 4 are colour 1; nodes 2 and 3 are colour 2. My understanding is that simply switching labels within colours is an isomorphism?
Thanks, Louis On 12 September 2012 14:49, Gábor Csárdi <[email protected]> wrote: > 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 _______________________________________________ igraph-help mailing list [email protected] https://lists.nongnu.org/mailman/listinfo/igraph-help
