Dfs algorithm and cycles question Is it true or false that for running a dfs on an undirected graph G with a simple cycle than this cycle will have exactly one back edge?

Looks to me likes its true ,is it?
No, it is not true. Consider the graph with vertices 1, 2, 3, 4, 5, 6 and edges 12, 23, 34, 45, 46, 56, 61. The dfs starting at vertex 1 yields two back egdes for the cycle (1,2,3,4,6).