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## [igraph] Graph isomorphism missed?

**From**: |
Louis Aslett |

**Subject**: |
[igraph] Graph isomorphism missed? |

**Date**: |
Wed, 12 Sep 2012 14:22:17 +0100 |

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] Graph isomorphism missed?**,
*Louis Aslett* **<=**