On the signature of a Lefschetz fibration coming from an involution

In this article we show that the signature of a Lefschetz fibration coming from a special involution as a product of right-handed Dehn twists depends only on the number of genus on the involution axis. We investigate the geography of such Lefschetz fibrations and we identify it with a blow up of a ruled surface. We also get a geography of the Lefschetz fibration coming from a finite order element of mapping class group as a composition of two special involutions.