Turkish Journal of Mathematics
DOI
10.3906/mat-1405-67
Abstract
We give explicit expressions of the Tutte polynomial of asymmetric complete flower graph and asymmetric incomplete flower graph. We then express these Tutte polynomials as generating functions and decode some valuable information about the asymmetric complete flower graph and asymmetric incomplete flower graph. Furthermore, we convert the Tutte polynomials into coboundary polynomials and give explicit expressions of the $k$-defect polynomials of these structures. Finally, we conclude that nonisomorphic graphs in this class have the same Tutte polynomials, the same chromatic polynomials, and the same defect polynomials.
Keywords
Tutte polynomial, cycle graph, flower graph, coboundary polynomials, $k$-defect polynomials
First Page
706
Last Page
718
Recommended Citation
MPHAKO-BANDA, EUNICE and MANSOUR, TOUFIK
(2015)
"Defect polynomials and Tutte polynomials of some asymmetric graphs,"
Turkish Journal of Mathematics: Vol. 39:
No.
5, Article 9.
https://doi.org/10.3906/mat-1405-67
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss5/9
