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.