graph theory count the number of nonisomorphic 6regular grap

graph theory

count the number of non-isomorphic 6-regular graphs on 9 vertices. (Hint:look at complement graph, 2-regular graph on 9 vertices)

Solution

2 regular graph on 9 vertices is a cycle. hence if there are 2 non-isomorphic graphs then the complements must also be non isomorphic but any 6-regular graph on 9 vertices provides same cyclic graph hence all such graphs are isomorphic.