Iranian Journal of Mathematical Chemistry

Iranian Journal of Mathematical Chemistry

Kirchhoff‎, ‎Multiplicative and Additive Degree-Kirchhoff Indices in Random Cyclodecane Chains

Document Type : Research Paper

Authors
Xuan Jiang 1
Pingping Chen 2
Kai Zhou 3
Duoduo Zhao 3
1 Department of Data Science‎, ‎Anhui University of Technology‎ , ‎Maanshan‎, ‎243032‎, ‎Anhui‎, ‎China
2 School of Mathematics and Statistics‎, ‎Beijing Technology and Business University‎, ‎Beijing‎, ‎100048‎, ‎China
3 School of Big Data and Artificial Intelligence‎, ‎Center of Applied Mathematics‎, ‎Chizhou University‎, ‎Chizhou‎, ‎247000‎, ‎Anhui‎, ‎China
10.22052/ijmc.2026.257678.2073
Abstract
‎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.
Keywords
Random cyclodecane chain, Kirchhoff index, Multiplicative degree-Kirchhoff index&lrm
, Additive degree-Kirchhoff index, Expected value, Recursive method
Subjects
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Iranian Journal of Mathematical Chemistry
Volume 17, Issue 3
In Progress
Summer 2026
Pages 287-306