Graphs-vertices and cycle length

Reference no: EM13123022

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

Reference no: EM13123022

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