The Adjacency Matrix of Three Sequences of Fullerenes
محورهای موضوعی : Combinatorics, Graph theory
O. Nekooei
1
(Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran)
H. Barzegar
2
(Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran)
A. Ashrafi
3
(Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran)
M. Ghorbani
4
(Department of mathematics, Islamic Azad University, Shahr-e-Qods Branch, Tehran, Iran)
کلید واژه: Adjacency matrix, $C_{12m+2}$, $C_{12m+4}$, $C_{12m+6}$,
چکیده مقاله :
when we study chemical graphs, the adjacency matrix is an important invariant of a graph with chemical meaning. In this paper, the general form of the adjacency matrices of three Sequences of Fullerenes will be determined.
\bibitem{1} Cantoni, A.; Buter, P. Eigenvalues and Eigenvectors of Symmetric Centrosymmetric Matrices.
{\it Linear Algebra Appl.,} {\bf 1976,} {\it 13}, 275-288.
\bibitem{3} Heinig, G.; Rost, K. Centrosymmetric and centro-skewsymmetric Toeplitz-plus-
Hankel matrices and Bezoutians. {\it Linear Algebra Appl.,} {\bf 2023,}{ \it 336}, 257–281.
\bibitem{4} Katona, G.Y.; Faghani, M.; Ashrafi, A. R. Centrosymmetric graphs and lower bound for graph energy of fullerene. {\it Discuss. Math. Graph Theory.,} {\bf 2014,} {\it 34,} 751-768.
\bibitem{5} Kroto, H. W.; Fichier, J. E.; Cox, D. E. \textit{The Fullerene, Pergamon press}, New York, 1993.
\bibitem{6} Graver, J. {\it Catalog of all fullerenes with ten or more symmetries}, {graphs and discovery,
DIMACS ser. discrete Math theoret comput sci, American Mathematical Society, Providence,} 2005, p. 167–188.
\bibitem{7} Ghorbani, M.; Songhori, M.; Ashrafi, A. R.; Graovac, A. Symmetry Group of (3,6)-Fullerenes, {\it Fullerenes, Nanotubes and Carbon Nanostructures.} {\bf 2015,} {\it 23,} 788-791.
\bibitem{8} Biggs, N. \textit{Algebraic Graph Theory}, $2^{nd}$ edition, { Cambridge Mathematical Library, Cambridge University Press, Cambridge}, 1993.
\bibitem{9} Nekooei, O.; Barzegar, H.; Ashrafi, A. R. Permanents of Hexagonal and Armchair Chains. {\it International Journal of Mathematics and Mathematical Sciences.} {\bf 2022}, ID 7786922.
\bibitem{9} Nekooei, O.; Barzegar, H. The adjacency matrix of some hexagonal systems. {\it Journal of Discrete Mathematics and Its Applications.} {\bf 2023}, {\it 8}(3), 165–173.
\bibitem{10} Fowler, P. W.; Manolopoulos, D. E. {\it An Atlas of Fullerenes}, Oxford University Press, Oxford, 1995.
