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On cyclic edge-connectivity of fullerenesKutnar, Klavdija, 1980- ; Marušič, DraganA 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 ▫$F$▫.Source: Discrete applied mathematics. - ISSN 0166-218X (Vol. 156, iss. 10, 2008, str. 1661-1669)Type of material - article, component part ; adult, seriousPublish date - 2008Language - englishCOBISS.SI-ID - 2017765
Author
Kutnar, Klavdija, 1980- |
Marušič, Dragan
Topics
teorija grafov |
fulereni |
povezanost |
Hamiltonov cikel |
popolno prirejanje |
graph |
fullerene graph |
cyclic edge-connectivity |
hamilton cycle |
perfect matching
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Kutnar, Klavdija, 1980- | 24997 |
Marušič, Dragan | 02887 |
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