Let G be a 2n−vertices simple graph such that in any partition of the set of vertices of G into two n−vertices sets V1 and V2, the number of edges from a vertex in V1 to another vertex in V1 is equal to the number of edges from a vertex in V2 to another vertex in V2. Prove that all the vertices have equal degrees. geometrygeometric transformationgraph theorycombinatorics proposedcombinatorics