Molecular electric conductance and long-bond structure counting for conjugated-carbon nano-structures

A graph theoretical index, here called a long-bond index (or a generalized Pauling bond order), predicts well the degree of electric conductance for (carbon sheet and carbon cylinder-shaped) molecular nano-structures. Some results are compared with those by means of molecular-orbital-theoretic Green’s function methods. The present alternative method is based on long-bond (or excited) structure counting as suggested from valence bond resonance theoretic ideas.