I developed an algorithm that transforms any simple connected graph, cyclic or not, into a tree. The resulting tree is syntax-preserving, in a sense that it allows to reconstruct the original input graph and only the original input graph. In other words, the constructed tree preserves adjacency information, while resolving cycles. Moreover, I assume that with the constructed tree allowing to reconstruct only the original input graph, no other graph that is structurally different can exist that would result in an identical tree form.
I did some research on algorithms that transform graphs into tree form, but I was unable to find another algorithm that would work for any simple connected graph like described above. However, I am pretty such there must exist something.
So maybe one more experienced in graph theory can help me out. It would be highly appreciated.