A cycle is defined to be a circuit with no repeasted vertex. If a cycle has length k, we talk of a k-cycle. Determine the number of 4-cycles in Km,n where m > 2 and n > 2.
I'm not a graph theorist, but I think since we are considering for , then any four distinct vertices -- 2 coming from the set of m vertices and 2 coming from the set of n vertices -- will make a 4-cycle. So that there will be ways of choosing such a collection of 4 vertices.