# Talk:Dyck graph

## Toroidal?

Are we sure this graph is toroidal? According to [1] it has genus 3. Maproom (talk) 22:24, 7 September 2009 (UTC)

- The dual graph of the torus embedding of the Shrikhande graph shown at right is clearly a symmetric cubic 32-vertex graph, and the Foster census says that the Dyck graph is the unique symmetric cubic 32-vertex graph. It may well also be true, as the link you give states, that the Dyck graph has a different genus-3 embedding with dual graph
*K*_{4,4,4}but I don't see where it states that to be the minimum-genus embedding. —David Eppstein (talk) 22:44, 7 September 2009 (UTC)

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