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Are these two graphs EQUAL to each other?

Exactly If a Graph contains the left graph in image as a sub-graph then it can not be an edge graph. the question is about the right one, Is it equal with left one? if yes, then does it mean If a Graph contains the right graph in image as a sub-graph too then it can not be an edge graph because it is the same as left one?

Please help me solve this small problem :)

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# Equality of the two graphs

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