I'm interested in finding graphs with certain properties, like the smallest cubic bipartite asymmetric graph. While working on a related graph-theoretic problem, concerning edge-colrings, I came along Georges Graph at Wolfram|Alpha.

It shows a nice collection of properties of the graph:

asymmetric | bicolorable | biconnected | bicubic | bipartite | bridgeless | class 1 | connected | cubic | cyclic | local | noncayley | noneulerian | nonhamiltonian | nonplanar | perfect | perfect matching | regular | square-free | traceable | triangle-free | weakly regular

So I'm interested if it's possible to search Wolfram|Alpha for graph with certain properties.

How to build a query, that returns a list of graphs that are asymmetric, bicubic and $3$-edge colorable i.e. they have chromatic index $3$?

Other ways to get that list are also welcome..

Cross-posted: http://mathematica.stackexchange.com/q/72628/1436