This will depend on the Markov order of the n-gram model.
intuitively, since the first dimension of the T, T weights is 0 for n-gram arcs and > 0 for backoff arcs, the shortest path will traverse the fewest possible backoff arcs; further, since higherorder backoff arcs cost less in the first dimension of the T, T weights in M , the shortest path will include n-gram arcs at their earliest possible point.