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bgsu1180115123.pdf (462.13 KB)
ETD Abstract Container
Abstract Header
The classification of l
1
-embeddable fullerenes
Author Info
Marcusanu, Mihaela C
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1180115123
Abstract Details
Year and Degree
2007, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Mathematics (Pure).
Abstract
In Chemistry, fullerenes are molecules composed entirely of carbon atoms, in the form of a hollow sphere, ellipsoid or tube, such that each atom is bonded with three other atoms and the atoms form pentagonal or hexagonal rings. The spherical fullerenes motivated the related mathematical concept: a fullerene graph is a trivalent plane graph such that all faces are pentagons and hexagons. The goal of this research is to prove the conjecture that there are exactly five l
1
-embeddable fullerenes. These are known to be the following fullerenes: F
20
(I
h
),F
26
(D
3h
), F
40
(T
d
), F
44
(T), F
80
(I
h
) (where the group of symmetry is given in parentheses for each fullerene). We proceed in proving this result by looking at the minimal distance between the pentagonal faces of the fullerene. In the cases when the minimal distance between pentagons is greater than two we obtain a contradiction, which leads us to conclude that in an l
1
-embeddable fullerene there must exist at least two pentagons that either are adjacent or have a common hexagonal neighbor. For the latter cases we show that the only possibilities are the five fullerenes listed above.
Committee
Sergey Shpectorov (Advisor)
Subject Headings
Mathematics
Keywords
fullerenes
;
l
1
-embeddable
;
graph
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Citations
Marcusanu, M. C. (2007).
The classification of l
1
-embeddable fullerenes
[Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1180115123
APA Style (7th edition)
Marcusanu, Mihaela.
The classification of l
1
-embeddable fullerenes.
2007. Bowling Green State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1180115123.
MLA Style (8th edition)
Marcusanu, Mihaela. "The classification of l
1
-embeddable fullerenes." Doctoral dissertation, Bowling Green State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1180115123
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
bgsu1180115123
Download Count:
639
Copyright Info
© 2007, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.