On the fundamental cycle set graph
Maciej M. Sysło · IEEE Transactions on Circuits and Systems · 1982
We prove that there exists a one-to-one correspondence between the spanning trees and the fundamental cycle sets of a graphGif and only ifGis 3-edge connected. Then we define a fundamental cycle set graph and prove that such a graph is a tree graph. It follows, therefore, that every fundamental cycle set graph on at least three vertices is Hamiltonian.