Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff in...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7523214 |
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| _version_ | 1832555160562302976 |
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| author | Shouliu Wei Wai Chee Shiu Xiaoling Ke Jianwu Huang |
| author_facet | Shouliu Wei Wai Chee Shiu Xiaoling Ke Jianwu Huang |
| author_sort | Shouliu Wei |
| collection | DOAJ |
| description | Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons. |
| format | Article |
| id | doaj-art-f696d77cec6541caa9fe90ca89ab982b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f696d77cec6541caa9fe90ca89ab982b2025-02-03T05:49:28ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/7523214Comparison of the Wiener and Kirchhoff Indices of Random PentachainsShouliu Wei0Wai Chee Shiu1Xiaoling Ke2Jianwu Huang3College of Mathematics and Data Science (Software College)College of Global TalentsCollege of Mathematics and Data Science (Software College)College of Mathematics and Data Science (Software College)Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons.http://dx.doi.org/10.1155/2021/7523214 |
| spellingShingle | Shouliu Wei Wai Chee Shiu Xiaoling Ke Jianwu Huang Comparison of the Wiener and Kirchhoff Indices of Random Pentachains Journal of Mathematics |
| title | Comparison of the Wiener and Kirchhoff Indices of Random Pentachains |
| title_full | Comparison of the Wiener and Kirchhoff Indices of Random Pentachains |
| title_fullStr | Comparison of the Wiener and Kirchhoff Indices of Random Pentachains |
| title_full_unstemmed | Comparison of the Wiener and Kirchhoff Indices of Random Pentachains |
| title_short | Comparison of the Wiener and Kirchhoff Indices of Random Pentachains |
| title_sort | comparison of the wiener and kirchhoff indices of random pentachains |
| url | http://dx.doi.org/10.1155/2021/7523214 |
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