Shell Polynomial of some graphs

Let G= (V,E) be a connected simple graph with the vertex set V(G) and edge set E(G) Define the entries in a Shell matrix ShM as [ShM]t,k= ∑v|div=k[M]I,v where M is any square topological matrix (info matrix). The Shell matrix is the collection of the above defined entries: ShM={[ShM]i,k ; iϵV(G); kϵ [0,1,2,..., d(G)]} where d(G) is the diameter of G and the zero column [ShM)i,0 is the diagonal entries in the info matrix M. The Shell polynomial is ShM(x)= ∑kP (G,k). xk with p(G,k)being sets of loca contributions (of extent k) to the global property p(G)= U p(G,k) and summation running up to d(G). The polynomial coefficients are obtain from the above defined Shell matrices, as the half sum of columns. The Cluj-Tehran index is defined as CT(ShM,G)= ShMi(1)+ 1/2 ShM11(1).

Keywords:

Shell polynomial , Cluj-Tehran index , nanotube