For HW, I need to find the number of isomorphic classes of a simple graph with 7 vertices, each with degree two. I know I could brute-force it by finding all edge sets that fulfill that criteria, but there must be a more efficient way. So, it there a formula that determines number of isomorphic classes of a simple graph with homogenous degree sequence? If my terminology is off, I appreciate your correction.
[Math] How to determine number of isomorphic classes of simple graph with n vertices, each with degree m
graph theorygraph-isomorphism
Best Answer
Hint: A 2-regular graph is a disjoint union of cycles. From there it should be fairly easy to see there are only 2 simple 2-regular graphs on 7 vertices.