The limiting behaviors for the Gutman index and the Schultz index in a random (2k + 1)-polygonal chain

Abstract

The exact formulae for the variances of the Gutman index and the Schultz index of a random (2k + 1)-polygonal chain is obtained in this paper. We also show that these two indices of a random (2k + 1)-polygonal chain obey normal distributions asymptotically. We expanded on several previously published findings. We apply the unified formulae to get the limiting behaviors of the Gutman index and the Schultz index of a specific random polygonal chain, which have been extensively explored in statistical physics and organic chemistry.