PI Polynomial of V-Phenylenic Nanotubes and Nanotori

摘要

The PI polynomial of a molecular graph is defined to be the sum X^{|E(G)|−N(e)} + |V(G)|(|V(G)|+1)/2 − |E(G)| over all edges of G, where N(e) is the number of edges parallel to e. In this paper, the PI polynomial of the phenylenic nanotubes and nanotori are computed. Several open questions are also included.