In the theory of total Tc-electron energy (E) an auxiliary quantity is defined via gamma* = [n(2mn - E-2)]/ [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 gamma* and n is observed, apparently contradicting to the way in which gamma* (by definition) depends on n, m, E. We now establish the condition which E must satisfy, in order that gamma* be a linear function of n: the condition for an exact linear relation between - and n is E = m.