Abstract Let *G=(V,E)* be a simple connected molecular graph. *Khadikar **et.al*. introduced the *PI* index defined by , where is the number of vertices of *G* lying closer to *u* and is the number of vertices of *G* lying closer to *v*. In this paper, we compute a closed formula of vertex PI index for Polycyclic Aromatic hydrocarbons.

**Keywords **Poly Aromatic Hydrocarbons *PAHk* ; PI index; Cut Method; Orthogonal Cut.