On the 2-factor index of a graph

The 2-factor index of a graph G  , denoted by f(G),f(G), is the smallest integer m such that the m  -iterated line graph Lm(G)Lm(G) of G   contains a 2-factor. In this paper, we provide a formula for f(G)f(G), and point out that there is a polynomial time algorithm to determine f(G)f(G).