  We discuss relation between three different methods to identify topologically
distinct short-range valence-bond ground states in spin-$\frac12$ two-leg
ladders: the string order parameters, the level-crossing method, and the
ground-state expectation value of the twist operator. For this purpose we
reexamine a phase transition in the frustrated spin ladder. We propose a proper
bosonization of the string order parameters. Then, these three methods are
shown to be equivalent reflecting the $Z_2\times Z_2$ symmetry breaking of the
order and the disorder fields of the two-dimensional Ising model.
