On cyclic edge-connectivity of fullerenes

Kutnar, Klavdija; Marušič, Dragan

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Title:	On cyclic edge-connectivity of fullerenes
Authors:	ID Kutnar, Klavdija (Author) ID Marušič, Dragan (Author)
Files:	http://dx.doi.org/10.1016/j.dam.2007.08.046
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
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 ▫$F$▫.
Keywords:	graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching
Year of publishing:	2008
Number of pages:	str. 1661-1669
Numbering:	Vol. 156, iss. 10
PID:	20.500.12556/RUP-7718
ISSN:	0166-218X
UDC:	519.17:541
DOI:	10.1016/j.dam.2007.08.046
COBISS.SI-ID:	2017765
Publication date in RUP:	03.04.2017
Views:	2138
Downloads:	138
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