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CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2

Year 2012, Volume: 41 Issue: 2, 277 - 282, 01.02.2012

Abstract

A graph is called edge-transitive if its automorphism group acts transitively on its set of edges. In this paper we classify all connected cubic edge-transitive graphs of order 14p 2 , where p is a prime.

References

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  • Conder, M. Trivalent (cubic) symmetric graphs on up to 2048 vertices, 2006. http://www.math.auckland.ac.nz/∼conder/∼conder/symmcubic2048list.txt.
  • Conder, M. and Nedela, R. A refined classification of cubic symmetric graphs, Jornal of Algebra 322, 722–740, 2009.
  • Conder, M and Malniˇc, A., Maruˇsiˇc, D. and Potoˇcnik, P. A census of semisymmetric cubic graphs on up to 768 vertices, J. Algebr. Comb. 23, 255–294, 2006.
  • Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A. An ATLAS of Finite Groups (Oxford University Press, Oxford, 1985).
  • Djokovi´c, ˇZ. D. and Miller, G. L. Regular groups of automorphisms of cubic graphs, J. Com- bin. Theory Ser. B 29, 195–230, 1980.
  • Du, S. F. and Xu, M. Y. A classification of semisymmetric graphs of order 2pq, Com. in Algebra 28 (6), 2685–2715, 2000.
  • Feng, Y. Q. and Kwak, J. H. On regular cubic graphs of order a small number times a prime or a prime square, J. Aust. Math. Soc. 76, 345–356, 2004.
  • Feng, Y. Q. and Kwak, J. H. Classifying cubic symmetric graphs of order 10p or 10p2, Sci. China Ser. A. Math. 49, 300–319, 2006.
  • Feng, Y. Q. and Kwak, J. H. Cubic symmetric graphs of order twice an odd prime-power, J. Aust. Math. Soc. 81, 153–164, 2006.
  • Feng, Y. Q. and Kwak, J. H. Cubic symmetric graphs of order a small number times a prime or a prime square, J. Combin. Theory Ser. B 97, 627–646, 2007.
  • Y. Q. Feng, J. H. Kwak and Xu, M. Y. Cubic s-regular graphs of order 2p3, J. Graph Theory , 341–352, 2006.
  • Folkman, J. Regular line-symmetric graphs, J. Combin. Theory 3, 215–232, 1967.
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  • Malniˇc, A., Maruˇsiˇc, D. and Potoˇcnik, P. Elementary abelian covers of graphs, J. Alg. Combin. 20, 71–97, 2004.
  • Malniˇc, A., Maruˇsiˇc, D. and Wang, C. Q. Cubic edge-transitive graphs of order 2p3, Discrete Math. 274, 187–198, 2004.
  • Oh, J. M. A classification of cubic s-regular graphs of order 14p, Discrete Math. 309, 2721– , 2009.
  • Rose, J. S. A Course On Group Theory (Cambridg University Press, Cambridge, 1978).
  • Tutte, W. T. A family of cubical graphs, Proc. Cambridge Philos. Soc. 43, 459–474, 1947.
  • Tutte, W. T. Connectivity in graphs (Toronto University Press, Toronto, 1966).
  • Wang, C. Q. and Chen, T. S. Semisymmetric cubic graphs as regular covers of K3,3, Acta Mathematica Sinica 24, 405–416, 2008.
  • Wang, C. Q. and Hao, Y. Edge-transitive regular Zn-covers of the Heawood graph, Discrete Mathematics 310, 1752–1758, 2010.
  • Wielandant, H. Finite Permutation Groups (Acadamic Press. New York, 1964).
  • Zhou, J. X. and Feng, Y. Q. Cubic vertex-transitive graphs of order 2pq, J. Graph Theory, DOI 10.1002/jgt.20481.

CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2

Year 2012, Volume: 41 Issue: 2, 277 - 282, 01.02.2012

Abstract

References

  • Alaeiyan, M. and Ghasemi, M. Cubic edge-transitive graphs of order 8p2, Bull. Austral. Math. Soc. 77,315–323, 2008.
  • Conder, M. Trivalent (cubic) symmetric graphs on up to 2048 vertices, 2006. http://www.math.auckland.ac.nz/∼conder/∼conder/symmcubic2048list.txt.
  • Conder, M. and Nedela, R. A refined classification of cubic symmetric graphs, Jornal of Algebra 322, 722–740, 2009.
  • Conder, M and Malniˇc, A., Maruˇsiˇc, D. and Potoˇcnik, P. A census of semisymmetric cubic graphs on up to 768 vertices, J. Algebr. Comb. 23, 255–294, 2006.
  • Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A. An ATLAS of Finite Groups (Oxford University Press, Oxford, 1985).
  • Djokovi´c, ˇZ. D. and Miller, G. L. Regular groups of automorphisms of cubic graphs, J. Com- bin. Theory Ser. B 29, 195–230, 1980.
  • Du, S. F. and Xu, M. Y. A classification of semisymmetric graphs of order 2pq, Com. in Algebra 28 (6), 2685–2715, 2000.
  • Feng, Y. Q. and Kwak, J. H. On regular cubic graphs of order a small number times a prime or a prime square, J. Aust. Math. Soc. 76, 345–356, 2004.
  • Feng, Y. Q. and Kwak, J. H. Classifying cubic symmetric graphs of order 10p or 10p2, Sci. China Ser. A. Math. 49, 300–319, 2006.
  • Feng, Y. Q. and Kwak, J. H. Cubic symmetric graphs of order twice an odd prime-power, J. Aust. Math. Soc. 81, 153–164, 2006.
  • Feng, Y. Q. and Kwak, J. H. Cubic symmetric graphs of order a small number times a prime or a prime square, J. Combin. Theory Ser. B 97, 627–646, 2007.
  • Y. Q. Feng, J. H. Kwak and Xu, M. Y. Cubic s-regular graphs of order 2p3, J. Graph Theory , 341–352, 2006.
  • Folkman, J. Regular line-symmetric graphs, J. Combin. Theory 3, 215–232, 1967.
  • Gross, J. L. and Tucker, T. W. Topological Graph Theory (Wiley-Interscience, New York, ). Lu, Z., Wang, C. Q. and Xu, M. Y. On semisymmetric cubic graphs of order 6p, Science in China Ser. A Mathematics 47 (1), 1–17, 2004.
  • Malniˇc, A., Maruˇsiˇc, D. and Potoˇcnik, P. Elementary abelian covers of graphs, J. Alg. Combin. 20, 71–97, 2004.
  • Malniˇc, A., Maruˇsiˇc, D. and Wang, C. Q. Cubic edge-transitive graphs of order 2p3, Discrete Math. 274, 187–198, 2004.
  • Oh, J. M. A classification of cubic s-regular graphs of order 14p, Discrete Math. 309, 2721– , 2009.
  • Rose, J. S. A Course On Group Theory (Cambridg University Press, Cambridge, 1978).
  • Tutte, W. T. A family of cubical graphs, Proc. Cambridge Philos. Soc. 43, 459–474, 1947.
  • Tutte, W. T. Connectivity in graphs (Toronto University Press, Toronto, 1966).
  • Wang, C. Q. and Chen, T. S. Semisymmetric cubic graphs as regular covers of K3,3, Acta Mathematica Sinica 24, 405–416, 2008.
  • Wang, C. Q. and Hao, Y. Edge-transitive regular Zn-covers of the Heawood graph, Discrete Mathematics 310, 1752–1758, 2010.
  • Wielandant, H. Finite Permutation Groups (Acadamic Press. New York, 1964).
  • Zhou, J. X. and Feng, Y. Q. Cubic vertex-transitive graphs of order 2pq, J. Graph Theory, DOI 10.1002/jgt.20481.
There are 24 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Mehdi Alaeiyan This is me

Mohsen Lashani This is me

Publication Date February 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 2

Cite

APA Alaeiyan, M., & Lashani, M. (2012). CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2. Hacettepe Journal of Mathematics and Statistics, 41(2), 277-282.
AMA Alaeiyan M, Lashani M. CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2. Hacettepe Journal of Mathematics and Statistics. February 2012;41(2):277-282.
Chicago Alaeiyan, Mehdi, and Mohsen Lashani. “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”. Hacettepe Journal of Mathematics and Statistics 41, no. 2 (February 2012): 277-82.
EndNote Alaeiyan M, Lashani M (February 1, 2012) CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2. Hacettepe Journal of Mathematics and Statistics 41 2 277–282.
IEEE M. Alaeiyan and M. Lashani, “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, pp. 277–282, 2012.
ISNAD Alaeiyan, Mehdi - Lashani, Mohsen. “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”. Hacettepe Journal of Mathematics and Statistics 41/2 (February 2012), 277-282.
JAMA Alaeiyan M, Lashani M. CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2. Hacettepe Journal of Mathematics and Statistics. 2012;41:277–282.
MLA Alaeiyan, Mehdi and Mohsen Lashani. “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, 2012, pp. 277-82.
Vancouver Alaeiyan M, Lashani M. CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2. Hacettepe Journal of Mathematics and Statistics. 2012;41(2):277-82.