On the Number of 3-Edge Colorings of Cubic Graphs

In this paper we present a short algebraic proof for a generalization of a formula of R. Penrose, Some applications of negative dimensional tensors, in: Combinatorial Mathematics and its Applications Welsh (ed.), Academic Press, 1971, pp. 221–244 on the number of 3-edge colorings of a plane cubic graph. We also show that the number of 3-edge colorings of cubic graphs can be computed (up to a factor of 2| E | / 3 − 1) by evaluating the Penrose polynomial of their cycle space at 4.