Topological Index as Applied to π-Electronic Systems. IV. On the Topological Factors Causing Non-Uniform π-Electron Charge Distribution in Non-Alternant Hydrocarbons

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Abstract The topological factors which cause non-uniform π-electron charge distribution in non-alternant hydrocarbons (NAH′s) are discussed. For estimating and analyzing the net-charge density a novel topological index, topological charge density, QrT, is proposed. It is defined as QrT=Re(FG,r(1)), the real part of FG,r(y)=Δr,r(iy)⁄Δ(iy), where Δ(x) is the secular determinant of graph G and Δr,r(x) is its adjunct with row r and column r struck out. This quantity QrT, corresponding to the Coulson net charge density Qr=1−qr, is related with the topological indices \widetildeZG and \widetildeYG which are defined in terms of the coefficients of the characteristic polynomial of graph G. As all the newly proposed indices can be enumerated graphically, one can easily estimate the net-charge densities of NAH′s.