Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index
In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex. Firstly, we discuss balanced bipartite graphs with δG≥t, where δG is the minimum...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2019/2047406 |
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| author | Guisheng Jiang Lifang Ren Guidong Yu |
| author_facet | Guisheng Jiang Lifang Ren Guidong Yu |
| author_sort | Guisheng Jiang |
| collection | DOAJ |
| description | In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex. Firstly, we discuss balanced bipartite graphs with δG≥t, where δG is the minimum degree of G, and gain some sufficient conditions for the graphs to be traceable or Hamiltonian, respectively. Secondly, we discuss nearly balanced bipartite graphs with δG≥t and present some sufficient conditions for the graphs to be traceable. Thirdly, we discuss graphs with δG≥t and obtain some conditions for the graphs to be traceable or Hamiltonian, respectively. Finally, we discuss t-connected graphs and provide some conditions for the graphs to be Hamilton-connected or traceable for every vertex, respectively. |
| format | Article |
| id | doaj-art-170239ba1ad3437581852ba9a3c226d6 |
| institution | Kabale University |
| issn | 2090-9063 2090-9071 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Chemistry |
| spelling | doaj-art-170239ba1ad3437581852ba9a3c226d62025-02-03T01:23:44ZengWileyJournal of Chemistry2090-90632090-90712019-01-01201910.1155/2019/20474062047406Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary IndexGuisheng Jiang0Lifang Ren1Guidong Yu2School of Physics and Electronic Engineering, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, ChinaIn this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex. Firstly, we discuss balanced bipartite graphs with δG≥t, where δG is the minimum degree of G, and gain some sufficient conditions for the graphs to be traceable or Hamiltonian, respectively. Secondly, we discuss nearly balanced bipartite graphs with δG≥t and present some sufficient conditions for the graphs to be traceable. Thirdly, we discuss graphs with δG≥t and obtain some conditions for the graphs to be traceable or Hamiltonian, respectively. Finally, we discuss t-connected graphs and provide some conditions for the graphs to be Hamilton-connected or traceable for every vertex, respectively.http://dx.doi.org/10.1155/2019/2047406 |
| spellingShingle | Guisheng Jiang Lifang Ren Guidong Yu Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index Journal of Chemistry |
| title | Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index |
| title_full | Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index |
| title_fullStr | Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index |
| title_full_unstemmed | Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index |
| title_short | Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index |
| title_sort | sufficient conditions for hamiltonicity of graphs with respect to wiener index hyper wiener index and harary index |
| url | http://dx.doi.org/10.1155/2019/2047406 |
| work_keys_str_mv | AT guishengjiang sufficientconditionsforhamiltonicityofgraphswithrespecttowienerindexhyperwienerindexandhararyindex AT lifangren sufficientconditionsforhamiltonicityofgraphswithrespecttowienerindexhyperwienerindexandhararyindex AT guidongyu sufficientconditionsforhamiltonicityofgraphswithrespecttowienerindexhyperwienerindexandhararyindex |