Graph Theory question about Electrical Networks on Bipartite Graphs

Graph Theory question about Electrical Networks on Bipartite Graphs

How can I find the effective resistance between any two points on a complete bipartite graph K_m,n I want to try and identify any equipotential points in order to simplify the problem, but Im not sure if Im doing this correctly. So far I think, if I have two nodes from the same partition of the graph, that I can contract the other partition yielding an effective resistance of frac2n where n is the size of the contracted partition. But when it comes to two vertices which are from different partitions of K_m,n, I cant seem to figure out how to simplify the problem.

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