A nontrivial graph G is called prime if G = G_1 x G_2 implies that G_1 or G_2 is trivial. Show that if a connected graph G has a vertex which is not in a cycle of length four, then G is prime.
where "x" is the cartesian product
Graphs, Vertices and Cycle Length are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.