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In this paper, we first introduce the explicit analytical formulas for the expected values of the Gutman and Schultz indices for a random cyclooctane chain COCn. Meanwhile, the explicit formulas of the variances of the Gutman and Schultz indices for a random cyclooctane chain are determined and we prove these two indices are asymptotically subject to normal distribution. Furthermore, we are surprised to find the expected values of the Sombor index SOCOCn, the reduced Sombor index RSOCOCn, the modified Sombor index mSOCOCn and the reduced and modified Sombor index mRSOCOCn for a random cyclooctane chain. [ABSTRACT FROM AUTHOR]

The study of topological indices of some special chemical graphs has become a hot topic in chemical theory. Let Ln be the dicyclobutadieno derivative of linear phenylene which consists of n hexagons and (n + 1) quadrangles and let Ln2 be the strong prism of the dicyclobutadieno derivative of linear phenylenes. Firstly, we obtain that the normalized Laplacian spectrum of Ln2 consists of the eigenvalues of symmetric matrices LA and LS according to the decomposition theorem of normalized Laplacian characteristic polynomial. Then, by taking full advantage of the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, we determine the explicit expressions of the multiplicative degree‐Kirchhoff index and the number of spanning trees of the graph Ln2. [ABSTRACT FROM AUTHOR]