The eccentric connectivity polynomial of two classes of nanotubes

In theoretical chemistry, the eccentric connectivity index ξ(G) of a molecular graph G   was introduced as ξ(G)=∑v∈V(G)d(v)ɛ(v)ξ(G)=∑v∈V(G)d(v)ɛ(v) where d(v) expresses the degree of vertex v and ɛ(v) is the largest distance between v and any other vertex of G  . The corresponding eccentric connectivity polynomial is denoted by ξ(G,x)=∑v∈V(G)d(v)xɛ(v)ξ(G,x)=∑v∈V(G)d(v)xɛ(v). In this paper, we present the exact expressions of eccentric connectivity polynomial for V-phenylenic nanotubes and Zig-Zag polyhex nanotubes.