Complete Characterization of Resistance Distance for Linear Octagonal Networks
Computing the resistance distance of a network is a fundamental and classical topic. In the aspects of considering the resistances between any two points of the lattice networks, there are many studies associated with the ladder networks and ladderlike networks. But the resistances between any two p...
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/5917098 |
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| author | Jing Zhao Jia-Bao Liu Ali Zafari |
| author_facet | Jing Zhao Jia-Bao Liu Ali Zafari |
| author_sort | Jing Zhao |
| collection | DOAJ |
| description | Computing the resistance distance of a network is a fundamental and classical topic. In the aspects of considering the resistances between any two points of the lattice networks, there are many studies associated with the ladder networks and ladderlike networks. But the resistances between any two points for more complex structures than ladder networks or ladderlike networks are still unknown. In this paper, a rather complicated structure which is named linear octagonal network is considered. Treelike octagonal systems are cata-condensed systems of octagons, which represent a class of polycyclic conjugated hydrocarbons. A linear octagonal network is a cata-condensed octagonal system with no branchings. Moreover, the resistances between any two points of a linear octagonal network are first determined. One finds that the effective resistances between new inserted points and others points of a linear octagonal network can be given by the effective resistances between two initial points which are inherited from the linear polyomino network. |
| format | Article |
| id | doaj-art-8bd0c8d0b0b94e48b0c252370c590230 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8bd0c8d0b0b94e48b0c252370c5902302025-02-03T01:28:34ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/59170985917098Complete Characterization of Resistance Distance for Linear Octagonal NetworksJing Zhao0Jia-Bao Liu1Ali Zafari2School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaDepartment of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-4697, Tehran, IranComputing the resistance distance of a network is a fundamental and classical topic. In the aspects of considering the resistances between any two points of the lattice networks, there are many studies associated with the ladder networks and ladderlike networks. But the resistances between any two points for more complex structures than ladder networks or ladderlike networks are still unknown. In this paper, a rather complicated structure which is named linear octagonal network is considered. Treelike octagonal systems are cata-condensed systems of octagons, which represent a class of polycyclic conjugated hydrocarbons. A linear octagonal network is a cata-condensed octagonal system with no branchings. Moreover, the resistances between any two points of a linear octagonal network are first determined. One finds that the effective resistances between new inserted points and others points of a linear octagonal network can be given by the effective resistances between two initial points which are inherited from the linear polyomino network.http://dx.doi.org/10.1155/2020/5917098 |
| spellingShingle | Jing Zhao Jia-Bao Liu Ali Zafari Complete Characterization of Resistance Distance for Linear Octagonal Networks Complexity |
| title | Complete Characterization of Resistance Distance for Linear Octagonal Networks |
| title_full | Complete Characterization of Resistance Distance for Linear Octagonal Networks |
| title_fullStr | Complete Characterization of Resistance Distance for Linear Octagonal Networks |
| title_full_unstemmed | Complete Characterization of Resistance Distance for Linear Octagonal Networks |
| title_short | Complete Characterization of Resistance Distance for Linear Octagonal Networks |
| title_sort | complete characterization of resistance distance for linear octagonal networks |
| url | http://dx.doi.org/10.1155/2020/5917098 |
| work_keys_str_mv | AT jingzhao completecharacterizationofresistancedistanceforlinearoctagonalnetworks AT jiabaoliu completecharacterizationofresistancedistanceforlinearoctagonalnetworks AT alizafari completecharacterizationofresistancedistanceforlinearoctagonalnetworks |