Mathematics – Combinatorics
Scientific paper
2007-02-17
Mathematics
Combinatorics
11 pages, 9 figures
Scientific paper
A graph is said to be cyclic $k$-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 cyclic 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 $15\cdot 2^{\lfloor \frac{n}{20}\rfloor}$ perfect matchings, where $n$ is the order of $F$.
Kutnar Klavdija
Marusic Dragan
No associations
LandOfFree
On Cyclic Edge-Connectivity of Fullerenes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Cyclic Edge-Connectivity of Fullerenes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Cyclic Edge-Connectivity of Fullerenes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-348388