|
" Matching in fullerene and molecular graphs "
/ Afshin Behmaram
2021/07/12
| center
|
:
|
دانشگاه تهران. کتابخانه پردیس علوم
|
| Document Type
|
:
|
Latin Dissertation
|
| Language of Document
|
:
|
English
|
| Record Number
|
:
|
1443063
|
| Doc. No
|
:
|
T61
|
| Call number
|
:
|
ر (L)-827
|
| Main Entry
|
:
|
Behmaram, Afshin
|
| Title & Author
|
:
|
Matching in fullerene and molecular graphs/ Afshin Behmaram
|
| College
|
:
|
: University Tehran--Faculty Mathematics--Studied Course Mathematics
|
| Date
|
:
|
, 2013
|
| Degree
|
:
|
Ph.D
|
| present date
|
:
|
2013
|
| field of study
|
:
|
Mathematics
|
| Page No
|
:
|
xi, 89, 15 p.: ill. (Thesis) + 1 CD-ROM (4 3/4 in.)
|
| Abstract
|
:
|
The firrst result of this thesis is a new upper bound for the number of perfect matching in pfaffian graphs. This upper bound is better than generalized Bregman's inequality. We show that some of our upper bounds are sharp for 3- and 4-regular pfaffian graphs. Then we apply our bound for fullerene graphs. Here, a fullerene graph is a 3-regular, 3-conected planar graph with pentagon or hexagon faces. In chemistry, fullerene is a molecule consisting entirely of carbon atoms. Each carbon is three-connected to other carbon atoms by one double and two single bonds. The set of double bonds in a fullerene is precisely a perfect matching in corresponding molecular graph. It turns out that the number of perfect matchings is highly related to the stability of the molecule. We prove that every circular fullerne have at most 20 $(n/12) perfect matchings. We also find expotential lower bound for the number of perfect matching in (3,6)-fullerenes. We further extend the definition of fullerene to m-generalized fullerene. A connected 3-regular planar graph G = (V;E) is called m-generalized fullerene if it has the following types of faces: two m-gons and all other pentagons and hexagons. Note that for m = 5; 6, m-generalized fullerene graphs are just ordinary fullerenes. As for fullerene graphs it is easy to show that the number of pentagons in m-generalized fullerene is 2m, while the number of hexagons is not determined. We found lower and upper bounds for the number of perfect matchings in a class of m-generalized fullerene. In Chapter 4, we find a formula for the number of paths of small size in fullerene graphs and we apply this relation for counting the number of matchings and independentsets of small size in fullerenes. We also extend this formula to (3,6)- and (4,6)-fullerenes. In Chapter 5, we describe distance property of fullerenes and some other molecular graphs. An exact formula for computing Wiener polarity in graphs without 3-cyclesand 4-cycles are obtained. Using this result, the Wiener polarity index of fullerene and some other molecular graphs are computed. Furthermore, some inequalities for the Wiener polarity index of graphs with restricted diameter are also presented. In Chapter 6, we count the number of perfect matchings in special class of TUC4C8 nanotubes with respect to the number of octahedron in each row and column and compute upper and lower bounds for the number of perfect matchings in general case. Finally, in the last chapter of this thesis, we find some properties of perfect matchings in the edge transitive graphs.
|
| Added Entry
|
:
|
Hassan Yousefi-Azari, Ali Reza Ashrafi , Supervisor
|
|
|
:
|
Yousefi-Azari, Hassan , Advisor
|
|
|
:
|
Ashrafi, Ali Reza , Advisor
|
| Added Entry
|
:
|
Tehran-- Mathematics-- Mathematics
|
| |