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Keywords = cyclooctatetraene chain

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18 pages, 324 KB  
Article
Computing the Number of s-Matchings in Cyclooctatetraene Chains
by Shiqin Chen, Hui Han and Xianya Geng
Symmetry 2024, 16(8), 951; https://doi.org/10.3390/sym16080951 - 25 Jul 2024
Cited by 2 | Viewed by 1409
Abstract
The Hosoya index is an important topological index in graph theory, which is defined as the total number of s-matchings, denoted as m(G,s), in a graph G. Therefore, computing the number of s-matchings for [...] Read more.
The Hosoya index is an important topological index in graph theory, which is defined as the total number of s-matchings, denoted as m(G,s), in a graph G. Therefore, computing the number of s-matchings for various molecular structures holds significant importance. By applying the concept of symmetry, defining the s-matching vector of the graph with a specified edge, using the transfer matrix, and iteratively applying two recursive formulas to derive the reduction formula, we compute the number of s-matchings of cyclooctatetraene chains. Full article
(This article belongs to the Section Mathematics)
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16 pages, 315 KB  
Article
Statistical Analyses of a Class of Random Cyclooctatetraene Chain Networks with Respect to Several Topological Properties
by Chen Tao, Shengjun Tang and Xianya Geng
Symmetry 2023, 15(11), 1971; https://doi.org/10.3390/sym15111971 - 24 Oct 2023
Cited by 1 | Viewed by 1255
Abstract
In recent years, the research on complex networks has created a boom. The objective of the present paper is to study a random cyclooctatetraene chain whose graph-theoretic mathematical properties arose scientists’ interests. By applying the concept of symmetry and probability theory, we obtain [...] Read more.
In recent years, the research on complex networks has created a boom. The objective of the present paper is to study a random cyclooctatetraene chain whose graph-theoretic mathematical properties arose scientists’ interests. By applying the concept of symmetry and probability theory, we obtain the explicit analytical expressions for the variances of Schultz index, multiplicative degree-Kirchhoff index Gutman index, and additive degree-Kirchhoff index of a random cyclooctatetraene chain with n octagons, which plays a crucial role in the research and application of topological indices. Full article
(This article belongs to the Special Issue Symmetry and Graph Theory)
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