The adjacency matrix of three sequences of fullerenes

محورهای موضوعی : Combinatorics, Graph theory

O. Nekooei ¹ , H. Barzegar ² , A. Ashrafi ³ , M. Ghorbani ⁴

1 - Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran
2 - Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran
3 - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran
4 - Department of mathematics, Islamic Azad University, Shahr-e-Qods Branch, Tehran, Iran

تاریخ دریافت : 1402/12/03 تاریخ پذیرش : 1403/02/23 تاریخ انتشار : 1403/02/25

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.

چکیده انگلیسی:

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.

منابع و مأخذ:

[1] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1993.

[2] A. Cantoni, P. Buter, Eigenvalues and eigenvectors of symmetric centrosymmetric matrices, Linear Algebra Appl. 13 (1976), 275-288.

[3] P. W. Fowler, D. E. Manolopoulos, An Atlas of Fullerenes, Oxford University Press, Oxford, 1995.

[4] M. Ghorbani, M. Songhori, A. R. Ashrafi, A. Graovac, Symmetry group of (3,6)-fullerenes, Fullerenes, Nanotubes and Carbon Nanostructures. 23 (2015), 788-791.

[5] G. Heinig, k. Rost, Centrosymmetric and centro-skewsymmetric Toeplitz-plus- Hankel matrices and Bezoutians, Linear Algebra Appl. 336 (2023), 257-281.

[6] G. Y. Katona, M. Faghani, A. R. Ashrafi, Centrosymmetric graphs and lower bound for graph energy of fullerene, Discuss. Math. Graph. Theory. 34 (2014), 751-768.

[7] H. W. Kroto, J. E. Fichier, D. E. Cox, The Fullerene, Pergamon Press, New York, 1993.

[8] O. Nekooei, H. Barzegar, A. R. Ashrafi, Permanents of hexagonal and armchair chains, Inter. J. Math. Math. Sci. (2022), 2022:7786922.