4 research outputs found
On Cyclic Edge-Connectivity of Fullerenes
A graph is said to be cyclic -edge-connected, if at least edges must
be removed to disconnect it into two components, each containing a cycle. Such
a set of edges is called a cyclic--edge cutset and it is called a
trivial cyclic--edge cutset if at least one of the resulting two components
induces a single -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 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 has
a Hamilton cycle, and as a consequence at least perfect matchings, where is the order of .Comment: 11 pages, 9 figure
Embeddability of open-ended carbon nanotubes in hypercubes
AbstractA graph that can be isometrically embedded into a hypercube is called a partial cube. An open-ended carbon nanotube is a part of hexagonal tessellation of a cylinder. In this article we determine all open-ended carbon nanotubes which are partial cubes