A concealed property of total π-electron energy

In the theory of total π-electron energy (E) an auxiliary quantity is defined via γ∗=[n(2mn−E2)]/[2m(2m+n−2E)], where n and m denote the number of vertices and edges of the molecular graph. Within classes of structurally similar conjugated systems a very good linear correlation between γ∗ and n is observed, apparently contradicting to the way in which γ∗ (by definition) depends on n,m,E. We now establish the condition which E must satisfy, in order that γ∗ be a linear function of n: the condition for an exact linear relation between γ∗ and n is E=m.