Graph theory: Prove that each cycle has minimum length of 5

[Has]

Hi, I'm a computer science student and I'm stuck with following problem:

How can I prove that indeed each cycle of this graph G has a minimum length of 5?

The following graph G is given:

I first have drawn some cycles in order to see whether indeed the minimum length is equal to 5. Then I was thinking in terms of planarity. Maybe if I see that G is planar, I can then draw an equivalent graph G' and see what is the minimum length of the graph. When I tested on planarity, I saw that G is not planar and therefor I'm now stuck with it.

Thank you.

 

[Deleted member 4993]

How can I prove that indeed each cycle of this graph G has a minimum length of 5?

The following graph G is given:

What are your thoughts?

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