Let  be a simple graph of order n with vertex set V and edge set E. Let  denote an unordered vertex pair of distinct vertices of G. The i-common neighbor set of G is defined as and  for  The polynomial  is defined as the common neighbor polynomial of G. In this paper, we study the common neighbor polynomial of some dendrimer structures. Also, we establish a relation between the common neighbor polynomial and Hosoya polynomial of triangle-free graphs of diameter not more than 3.

common neighbor polynomial, dendrimer.