University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 3 2026 09 01 Kirchhoff‎, ‎Multiplicative and Additive Degree-Kirchhoff Indices in Random Cyclodecane Chains 287 306 115736 10.22052/ijmc.2026.257678.2073 EN Xuan Jiang Department of Data Science‎, ‎Anhui University of Technology‎ , ‎Maanshan‎, ‎243032‎, ‎Anhui‎, ‎China Pingping Chen School of Mathematics and Statistics‎, ‎Beijing Technology and Business University‎, ‎Beijing‎, ‎100048‎, ‎China Kai Zhou School of Big Data and Artificial Intelligence‎, ‎Center of Applied Mathematics‎, ‎Chizhou University‎, ‎Chizhou‎, ‎247000‎, ‎Anhui‎, ‎China Duoduo Zhao School of Big Data and Artificial Intelligence‎, ‎Center of Applied Mathematics‎, ‎Chizhou University‎, ‎Chizhou‎, ‎247000‎, ‎Anhui‎, ‎China 0009-0003-0667-0478 Journal Article 2025 09 29 ‎The Kirchhoff index serves as a significant measure in characterizing molecular topological structures‎. ‎It quantifies atomic connectivity within molecules and facilitates the correlation and prediction of physicochemical properties and biological activities of chemical compounds‎, ‎thereby holding considerable practical value‎. ‎This paper derives recurrence relations for the expected values of three variants of the Kirchhoff index‎, ‎the multiplicative degree-Kirchhoff index‎, ‎and the additive degree-Kirchhoff index in random cyclodecane chains using a recursive approach‎. ‎Based on these relations‎, ‎the extremal values and average values of these indices are obtained for a cyclodecane chain composed of $n$ regular decagons‎. ‎Furthermore‎, ‎it is shown that the expected Kirchhoff indices of the random cyclodecane chain equal the average of the corresponding indices over five specific structural configurations of the chain‎. https://ijmc.kashanu.ac.ir/article_115736_35072f52eb0bc3efb2b1f5ca8cc2d822.pdf