How many cycles exist in a K5 graph with one edge missing?
are all K5 graphs with one edge missing isomorphic?
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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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
Total different cycles of 5 for k5 graph
Total different cycles of 4 for k5
Total different cycles of 3 for k5
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
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