On the basis of deleting theorem, the problem of isospectral graphs is treated uniformly:discriminating isospectral graphs and identifying isospectral points by means of graphical-deleting; constructing new isospectral graphs from the inverse process-expansion of weightedgraphs. Some methods of identifying isospectral points have been deduced newly and themethod of deriving isospectral graphs has been extended by using many pairs of isospectralpoints. In addition, we have made more discussions on isospectral graphs of chain moleculeswhich were handled only for a few cases and we also give some series of isospectral mole-cules.