Made Easy: Counting number of subgraphs of the given graph. How should I approach this question?

Question

Comments

Yes @tishhaagrawal you are right. For 5 vertices answer should be 32.

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@parth023 I think you are right, we will get only 15 subgraphs if we choose 2 vertices from the given graph.

But counting all the subgraphs present in the given graph using this approach will be very tedious, also we might miss some of the subgraphs in this approach!

The solution provided by Made Easy is surely wrong, but can you explain a systematic way to get to the answer, please

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@tishhaagrawal i’m getting 123 as answer, plus the best “systematic way” i can think is just go by number of vertices.may be there is some formula for counting number of sub-graphs in some special graphs like cycle or complete graph but i don’t know about that.