I have the following graph that is similar to Petersen's graph
I was wondering if the number of cycle subgraphs is 792.
Here are my arguments:
Since the graph has 10 vertices, the only possible cycle subgraphs have 3, 4, 5, or 6 vertices. The number of cycle subgraphs with 3 vertices is 10C3 = 120. The number of cycle subgraphs with 4 vertices is 10C4 = 210. The number of cycle subgraphs with 5 vertices is 10C5 = 252. The number of cycle subgraphs with 6 vertices is 10C6 = 210. Therefore, the total number of cycle subgraphs with 10 vertices is 120 + 210 + 252 + 210 = 792.