| Title: | On cyclic edge-connectivity of fullerenes |
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| Authors: | ID Kutnar, Klavdija (Author)
ID Marušič, Dragan (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.dam.2007.08.046
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫. |
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| Keywords: | graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching |
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| Year of publishing: | 2008 |
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| Number of pages: | str. 1661-1669 |
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| Numbering: | Vol. 156, iss. 10 |
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| PID: | 20.500.12556/RUP-7718  |
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| ISSN: | 0166-218X |
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| UDC: | 519.17:541 |
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| DOI: | 10.1016/j.dam.2007.08.046 |
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| COBISS.SI-ID: | 2017765 |
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| Publication date in RUP: | 02.04.2017 |
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| Views: | 2484 |
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| Downloads: | 140 |
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