The expected values for the Gutman index, Schultz index, and some Sombor indices of a random cyclooctane chain

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 p...

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Bibliographic Details
Published in:International journal of quantum chemistry 2023-02, Vol.123 (3), p.n/a
Main Authors: Liu, Jia‐Bao, Gu, Jiao‐Jiao, Wang, Kang
Format: Article
Language:English
Subjects:
Chains
Chemistry
expected value
modified Sombor index
Normal distribution
Physical chemistry
Quantum physics
random cyclooctane chain
reduced Sombor index
variance
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Summary: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.
ISSN:0020-7608
1097-461X
DOI:10.1002/qua.27022