Systematic studies were further made on graph theory in quantitative structure-spectrum relationships (QSSR) for various areas of spectroscopies. Chemical shifts (CS) in alkanes for carbon-13 nuclear magnetic resonance (13C NMR) were well correlated with a set of novel molecular graph indices, called the rooted path vector of various lengths, as several multivariate regression equations as following:CS=3.022+5.336P1+7.356P2-1.648P3+0.83859P4+0.210P5-0.138P6-0.506P7+2.486P8-1.669P9; n=402, m=9, R=0.944, RCV=0.9413, S.D.=3.333, F=358.343, U=35833.211, Q=4355.422 for all types (primary, secondly, tertiary, quaternary as well as methane) of carbon atoms CS=0.983+6.811P1+7.584P2-2.029P3+0.809P4+0.106P5+0.043P6-0.124P7+1.715P8-1.101P9; n=374, m=9, R=0.975, RCV=0.9737, S.D.=2.303, F=773.372, U=36912.109, Q=1930.363 for primary, secondly, tertiary (including methane) carbon atoms; and CS=27.819+2.351P2+0.549P3-0.440P4+0.170P5-0.050P6; n=27, m=5, R=0.992, RCV=0.9674, S.D.=0.324, F=265.418, U=138.891, Q=2.198 for quaternary carbon atoms, respectively. Quite good estimation and prediction results were obtained from the quantitative molecular modeling and the performance of multiple linear regression (MLR) equations were tested to work well through cross-validation (CV) with the leave-one-out (LOO) procedure.