Optimal Vertex Ordering of a Graph and its Application to Symmetry Detection

We consider in this paper the problem of optimal vertex ordering of a graph. The vertex ordering and an optimality measure are defined. It is proved that the optimal ordering problem can be transformed into the well-known minimum-weight spanning tree problem. Some properties of optimal vertex orderings are investigated. And finally, the application of the optimal vertex ordering technique to an algorithm for detecting the symmetry of polyhedra is discussed in some detail.

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