How many cycles exist in a K5 graph with one edge missing? are all K5 graphs with one edge missing isomorphic? Definitions a Kn graph is a graph with n vertices and all vertices are connected to each other (total number of edges possible with n vertices, nchoose2) a cycle has to start and end with the same vertex, and can only intersect all other vertices only once

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How many cycles exist in a K5 graph with one edge missing? are all K5 graphs with one edge missing isomorphic? Definitions a Kn graph is a graph with n vertices and all vertices are connected to each other (total number of edges possible with n vertices, nchoose2) a cycle has to start and end with the same vertex, and can only intersect all other vertices only once

Mathematics
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i was thinking of solving this more combinatorically
but id have to first know if all k5 graphs with 1 edge missing is infact isomorphic,
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oh ofcourse xD
okay so combinatorically i was thinking lets take every possible permutations 5! Total different cycles of 5 for k5 graph 5!/5 Total different cycles of 4 for k5 5!/4 Total different cycles of 3 for k5 5!/(2!*3) now from each case we must subtract where a certain edge is happening like since k5 is missing 1 edge then for example vertex 2 and 5 cannot appear each other, as going from 2 to 5 or from 5 to 2 is possible in a cycle
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m thinking of every permutation as being around a round table to make it look like a cycle, thats why i am dividing by the length of the cycle
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