Abstract
Abstract We have calculated exactly the number,the mean-square end-to-end distance, the mean-square radius of gyration, and the mean-square distance of a monomer from the origin for n step self-avoiding walks on the 4-8 lattices up to 40 steps by computer . We estimated the connective constant, critical expo-nents and critical amplitudes . The estimated values of the exp-onents and are quite close to 1.34375 and 0.75 respectively, as expected from the universality conjecture which pred-icts that self-avoiding walks on two-dimensional lattices have the same critical exponents . Our numerical results are consistent with the theoretical prediction by Cardy and Saleur on the universality for certain amplitude ratios .