Cycles and cocycles of fuzzy graphs
In this paper we show that if the fuzzy graph (σ,μ) is a cycle, then it is a fuzzy cycle if and only if (σ,μ) is not a fuzzy tree. We also examine the relationship between fuzzy bridges and cycles. We introduce and examine the concepts of chords, twigs, 1-chains with boundary zero, cycle vectors, co...
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| Veröffentlicht in: | Information sciences 1996, Vol.90 (1), p.39-49 |
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| creator | Mordeson, John N. Nair, Premchand S. |
| description | In this paper we show that if the fuzzy graph (σ,μ) is a cycle, then it is a fuzzy cycle if and only if (σ,μ) is not a fuzzy tree. We also examine the relationship between fuzzy bridges and cycles. We introduce and examine the concepts of chords, twigs, 1-chains with boundary zero, cycle vectors, coboundary, and cocycles for fuzzy graphs. We show that although the set of cycle vectors, fuzzy cycle vectors, cocycles, and fuzzy cocycles do not necessarily form vector spaces over the field
Z
2 of integers modulo 2, they nearly do. Thisallows us to introduce the concepts of (fuzzy) cycle rank and (fuzzy) cocycle rank for fuzzy graphs in a meaningful way. |
| doi_str_mv | 10.1016/0020-0255(95)00238-3 |
| format | Article |
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Z
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Z
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Z
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| ispartof | Information sciences, 1996, Vol.90 (1), p.39-49 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete - AutoHoldings |
| subjects | Applied sciences Computer science control theory systems Exact sciences and technology Information retrieval. Graph Theoretical computing |
| title | Cycles and cocycles of fuzzy graphs |
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