On the Merrifield-Simmons index and generating functions for the graphs of the state PL(2,n)

Abstract

In this study, we compute Merrifield-Simmons index of graphs which corresponds to PL (2, n) by using the decomposition formula. Examination shows that Merri-field-Simmons index of certain classes of graphs deduce as a result in a difference equation. Further, the prominent formula for Merrifield-Simmons index of PL (2, n) and generating function are found as a function of the number n of hexagons in the state of PL (2, n). Also the relations formed for the (PL (2, n, n)) graphs obtained by combining two PL (2, n) with a certain angle between them are given.