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

Yıl 2012, Cilt: 41 Sayı: 2, 277 - 282, 01.02.2012

Öz

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.

Kaynakça

  • 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.

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

Yıl 2012, Cilt: 41 Sayı: 2, 277 - 282, 01.02.2012

Öz

Kaynakça

  • 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.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Matematik
Yazarlar

Mehdi Alaeiyan Bu kişi benim

Mohsen Lashani Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 41 Sayı: 2

Kaynak Göster

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. Şubat 2012;41(2):277-282.
Chicago Alaeiyan, Mehdi, ve Mohsen Lashani. “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”. Hacettepe Journal of Mathematics and Statistics 41, sy. 2 (Şubat 2012): 277-82.
EndNote Alaeiyan M, Lashani M (01 Şubat 2012) CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2. Hacettepe Journal of Mathematics and Statistics 41 2 277–282.
IEEE M. Alaeiyan ve M. Lashani, “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”, Hacettepe Journal of Mathematics and Statistics, c. 41, sy. 2, ss. 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 (Şubat 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 ve Mohsen Lashani. “CLASSIFICATION OF CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 14p 2”. Hacettepe Journal of Mathematics and Statistics, c. 41, sy. 2, 2012, ss. 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.