On the automorphism group of cubic polyhedral graphs

Document Type: Original Article

Author

Department of Mathematics, Shahid Rajaee Teacher Training University

Abstract

In the present paper, we introduce the automorphism group of cubic polyhedral graphs whose faces are triangles, quadrangles, pentagons and hexagons.

Graphical Abstract

On the automorphism group of cubic polyhedral graphs

Keywords

Main Subjects


[1] D. Cvetkovic, P. Rowlinson, P. Fowler, D. Stevanovic, Constructing fullerene graphs from their eigenvalues and angles, Lin. Algebra Appl. 356 (2002) 37–56.
[2] D. Cvetkovic, D. Stevanovi ´ c, Spectral moments of fullerene graphs, MATCH Commun. Math. Comput. Chem. 50 (2004) 62–72.
[3] M. Dehmer, A. Mowshowitz, A History of Graph Entropy Measures, Information Sciences 1 (2011) 57–78.
[4] A. Deza, M. Deza, V. Grishukhin, Fullerenes and coordination polyhedral graph versus half cube embeddings, Discr. Math. 192 (1998) 41–80.
[5] M. Deza, M. Dutour, Zigzag structure of simple two-faced polyhedra, Combinatorics, Probability and Computing 14 (2005) 31–57.
[6] M. Deza, M. D. Sikiric, P. W. Fowler, The symmetries of cubic polyhedral graphs with face size no larger than 6, MATCH Commun. Math. Comput. Chem. 61 (2009) 589–602.
[7] T. Doslic, On lower bounds of number of perfect matchings in fullerene graphs, J. Math. Chem. 24 (1998) 359–364.
[8] T. Doslic, On some structural properties of fullerene graphs, J. Math. Chem. 31 (2002) 187–195.
[9] T. Doslic, Fullerene graphs with exponentially many perfect matchings, J. Math. Chem. 41 (2007) 183–192.
[10] P. W. Fowler, J. E. Cremona, Fullerenes containing fused triples of pentagonal rings, J. Chem. Soc. Faraday 93 (1997) 2255-2262.
[11] P. W. Fowler, D. E. Manolopoulos, D. B. Redmond, R. Ryan, Possible symmetries of fullerenes structures, Chem. Phys. Lett. 202 (1993) 371–378.
[12] R. Frucht: Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Mathemat-ica 6 (1938) 239–250.
[13] M. Ghorbani, E. Bani-Asadi, Remarks on characteristic coefficients of fullerene graphs, Appl. Math. Comput. 230 (2014) 428–435.
[14] M. Ghorbani, M. Songhori, A. R. Ashrafi, A. Graovac, Symmetry group of (3,6)-fullerenes, Fullerenes, Nanotubes and Carbon Nanostructures 23 (2015) 788–791.
[15] M. Ghorbani, M. Songhori, On the automorphism group of polyhedral graphs, App. Math. Com-put. 282 (2016) 237–243.
[16] J. E. Graver, Kekule structures and the face independence number of a fullerene, Eur. J. Combin. 28 (2007) 1115–1130.

[17] J. E. Graver, Encoding fullerenes and geodesic domes, SIAM. J. Discr. Math. 17 (2004) 596–614.
[18] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, R. E. Smalley, C60: Buckminster fullerene Nature
318 (1985) 162–163.
[19] H. W. Kroto, J. E. Fichier, D. E Cox, The Fulerene, Pergamon Press, New York, 1993.
[20] K. Kutnar, D. Marusic, On cyclic edge-connectivity of fullerenes, Discr. Appl. Math. 156 (2008) 1661–1669.
[21] K. Kutnar, D. Marusic, D. Janezic, Fullerenes via their automorphism groups, MATCH Commun. Math. Comput. Chem. 63 (2010) 267–282.