Sadhana polynomial in nano-dendrimers

Sadhana polynomial is defined on the ground of quasi orthogonal cut qoc strips in a graph G = G(V, E). A qoc strip, defined with respect to any edge in G, represents the smallest subset of edges closed under taking opposite edges on faces. The first derivative, in x = 1, of Sadhana polynomial is a multiple of the number of edges in the graph. Dendrimers are hyper-branched macromolecules, with a rigorously tailored architecture. In high generation dendrimers, it is difficult to calculate this polynomial. Thus, the composition of the global polynomial by monomeric contributions would facilitate the computation. Composition rule for in a family of nano-dendrimers, according to their topology, is derived.