Connectivity Analysis of Cyclically Balanced Fuzzy Graphs
The concepts of connectivity and cycle connectivity play an important role in fuzzy graph theory. In this article, cyclic cutvertices, cyclic bridges and cyclically balanced fuzzy graphs are discussed. It is proved that a vertex in a fuzzy graph is a cyclic cutvertex if and only if it is a common ve...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Tsinghua University Press
2015-06-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1616865815000473 |
| _version_ | 1797707095822303232 |
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| author | N. Jicy Sunil Mathew |
| author_facet | N. Jicy Sunil Mathew |
| author_sort | N. Jicy |
| collection | DOAJ |
| description | The concepts of connectivity and cycle connectivity play an important role in fuzzy graph theory. In this article, cyclic cutvertices, cyclic bridges and cyclically balanced fuzzy graphs are discussed. It is proved that a vertex in a fuzzy graph is a cyclic cutvertex if and only if it is a common vertex of all strong cycles with maximum strength. Also a cyclic cutvertex cannot be a fuzzy endvertex in a fuzzy graph. A characterization of cyclically balanced fuzzy graphs is obtained. Cyclic vertex connectivity and cyclic edge connectivity of fuzzy graphs are also discussed. |
| first_indexed | 2024-03-12T06:02:20Z |
| format | Article |
| id | doaj.art-e793ca1a509042f48354dbf35496bc59 |
| institution | Directory Open Access Journal |
| issn | 1616-8658 |
| language | English |
| last_indexed | 2024-03-12T06:02:20Z |
| publishDate | 2015-06-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-e793ca1a509042f48354dbf35496bc592023-09-03T04:06:58ZengTsinghua University PressFuzzy Information and Engineering1616-86582015-06-017224525510.1016/j.fiae.2015.05.008Connectivity Analysis of Cyclically Balanced Fuzzy GraphsN. JicySunil MathewThe concepts of connectivity and cycle connectivity play an important role in fuzzy graph theory. In this article, cyclic cutvertices, cyclic bridges and cyclically balanced fuzzy graphs are discussed. It is proved that a vertex in a fuzzy graph is a cyclic cutvertex if and only if it is a common vertex of all strong cycles with maximum strength. Also a cyclic cutvertex cannot be a fuzzy endvertex in a fuzzy graph. A characterization of cyclically balanced fuzzy graphs is obtained. Cyclic vertex connectivity and cyclic edge connectivity of fuzzy graphs are also discussed.http://www.sciencedirect.com/science/article/pii/S1616865815000473Fuzzy graphCyclic cutvertexCyclic bridgeCyclically balanced fuzzy graph |
| spellingShingle | N. Jicy Sunil Mathew Connectivity Analysis of Cyclically Balanced Fuzzy Graphs Fuzzy Information and Engineering Fuzzy graph Cyclic cutvertex Cyclic bridge Cyclically balanced fuzzy graph |
| title | Connectivity Analysis of Cyclically Balanced Fuzzy Graphs |
| title_full | Connectivity Analysis of Cyclically Balanced Fuzzy Graphs |
| title_fullStr | Connectivity Analysis of Cyclically Balanced Fuzzy Graphs |
| title_full_unstemmed | Connectivity Analysis of Cyclically Balanced Fuzzy Graphs |
| title_short | Connectivity Analysis of Cyclically Balanced Fuzzy Graphs |
| title_sort | connectivity analysis of cyclically balanced fuzzy graphs |
| topic | Fuzzy graph Cyclic cutvertex Cyclic bridge Cyclically balanced fuzzy graph |
| url | http://www.sciencedirect.com/science/article/pii/S1616865815000473 |
| work_keys_str_mv | AT njicy connectivityanalysisofcyclicallybalancedfuzzygraphs AT sunilmathew connectivityanalysisofcyclicallybalancedfuzzygraphs |