On walks in molecular graphs.

Walks in molecular graphs and their counts for a long time have found applications in theoretical chemistry. These are based on the fact that the (i, j)-entry of the kth power of the adjacency matrix is equal to the number of walks starting at vertex i, ending at vertex j, and having length k. In recent papers (refs 13, 18, 19) the numbers of all walks of length k, called molecular walk counts, mwc(k), and their sum from k = 1 to k = n - 1, called total walk count, twc, were proposed as quantities suitable for QSPR studies and capable of measuring the complexity of organic molecules. We now establish a few general properties of mwc's and twc among which are the linear dependence between the mwc's and linear correlations between the mwc's and twc, the spectral decomposition of mwc's, and various connections between the walk counts and the eigenvalues and eigenvectors of the molecular graph. We also characterize the graphs possessing minimal and maximal walk counts.     

拓扑-量子指数醛酮气相色谱保留指数及沸点的定量构效关系

通过对醛酮化合物分子结构特征及其气相色谱保留指数(RI)和沸点与分子结构间关系的研究,提出了分子极化效应指数(MPEI)、奇偶指数(OEI)、立体效应指数(SVij)、顶点度-距离指数(VDI)及键连接矩阵特征根(∑X1CH)等拓扑-量子结构参数,用多元线性回归(MLR)方法获得了醛酮类化合物的沸点及其在不同极性色谱柱上的气相色谱保留指数与这些拓扑-量子指数间良好的定量结构-性质相关(QSPR)模型,相关系数均大于0.99。5个分子结构参数具有明确的物理化学意义且易于计算和运用。与文献研究的比较结果表明:由上述分子结构参数得出的模型方程适用于各类醛酮化合物的气相色谱保留指数及沸点的预测且具有较好的稳定性和准确性。