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Original Articles

Automorphism Group of Generalized Cayley Graph of Upper Triangular Matrices

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Pages 4125-4137 | Received 03 Jun 2014, Published online: 06 Jul 2015

REFERENCES

  • Conder , M. , Lorimer , P. ( 1989 ). Automorphism groups of symmetric graphs of valency 3 . Journal of Combinatorial Theory, Series B 47 : 60 – 72 .
  • Dénes , J. ( 1967 ). Connections between Transformation Semigroups and Graphs . Theory of Graphs . New York–Paris : Gordon and Breach , pp. 93 – 101 .
  • Dobson , T. ( 2008 ). Automorphism Groups of Cayley Graphs. Available at: http://www.cs.uleth.ca/~morris/banff-symmetries/talks/Dobson-Banfftalk.pdf. Accessed March 15, 2014 .
  • Fan , S. H. , Zeng , Y. S. ( 2007 ). On Cayley graphs of bands . Semigroup Forum 74 : 99 – 105 .
  • Fang , X. ( 2002 ). On the automorphism groups of Cayley graphs of finite simple groups . Journal of the London Mathematical Society 66 : 563 – 578 .
  • Fang , X. , Ma , X. , Wang , J. ( 2011 ). On locally primitive Cayley graphs of finite simple groups . Journal of Combinatorial Theory, Series A 118 : 1039 – 1051 .
  • Feng , Y. ( 2006 ). Automorphism groups of Cayley graphs on symmetric groups with generating transposition sets . Journal of Combinatorial Theory, Series B 96 : 67 – 72 .
  • Ganesan , A. The automorphism group of Cayley graphs on symmetric groups generated by transposition sets and of the modified bubble-sort graph, Technical report. 19 pages, available at http://arxiv.org/abs/1205.5199, May 2012.
  • Godsil , C. ( 1981 ). On the full automorphism group of the graph . Combinatorica 1 : 243 – 256 .
  • Godsil , C. , Royle , G. ( 2001 ). Algebraic Graph Theory . Graduate Text in Mathematics , New York-Heidelberg : Springer-Verlag .
  • Hahn , G. ( 1981 ). The automorphism group of a product of hypergraphs . Journal of Combinatorial Theory, Series B 30 : 276 – 281 .
  • Imrich , W. , Watkins , M. E. ( 1976 ). On automorphism groups of Cayley graphs . Periodica Mathematica Hungarica 7 : 243 – 258 .
  • Jajcay , R. ( 2000 ). The structure of automorphism groups of Cayley graphs and maps . Journal of Algebraic Combinatorics 12 : 73 – 84 .
  • Kelarev , A. V. ( 2004 ). Labelled Cayley graphs and minimal automata . Australasian J. Combinatorics 30 : 95 – 101 .
  • Kelarev , A. V. ( 2003 ). Graph Algebras and Automata . New York : Marcel Dekker .
  • Kelarev , A. V. ( 2002 ). On undirected Cayley graphs . Australasian Journal of Combinatorics 25 : 73 – 78 .
  • Kelarev , A. V. ( 2006 ). On Cayley graphs of inverse semigroups . Semigroup Forum 72 : 411 – 418 .
  • Kelarev , A. V. , Praeger , C. E. ( 2003 ). On transitive Cayley graphs of groups and semigroups . European J. Combin. 24 : 59 – 72 .
  • Kelarev , A. V. , Quinn , S. J. ( 2003 ). A combinatorial property and Cayley graphs of semigroups . Semigroup Forum 66 : 89 – 96 .
  • Kelarev , A. V. , Ryan , J. , Yearwood , J. L. ( 2009 ). Cayley graphs as classifiers for data mining: The influence of asymmetries . Discrete Math. 309 : 5360 – 5369 .
  • Li , C. H. , Praeger , C. E. ( 1999 ). On the isomorphism problem for finite Cayley graphs of bounded valency . European J. Combin. 20 : 279 – 292 .
  • Li , C. H. , Praeger , C. E. ( 2001 ). Self-complementary vertex-transitive graphs need not be Cayley graphs . Bull. London Math. Soc. 33 : 653 – 661 .
  • Panma , S. , Chiangmai , N. , Knauer , U. , Arworn , Sr. ( 2006 ). Characterizations of Clifford semigroup digraphs . Discrete Math. 306 : 1247 – 1252 .
  • Praeger , C. E. ( 1997 ). Finite transitive permutation groups and finite vertex-transitive graphs . In: Graph Symmetry: Algebra Methods and Applications . Dordrecht : Kluwer , pp. 277 – 318 .
  • Praeger , C. E. (1999). Finite normal edge-transitive Cayley graphs. Bull. Austral. Math. Soc. 60:207–220.
  • Resmini , M. J. D. , Jungnickel , D. ( 1992 ). Strongly regular semi-Cayley graphs . J. Algebraic Combin. 1 : 171 – 195 .
  • Seifter , N. , Trofimov , V. I. ( 1997 ). Automorphism groups of graphs with quadratic growth . Journal of Combinatorial Theory, Series B 71 : 205 – 210 .
  • Stacey , K. C. , Holton , D. A. ( 1977 ). On the automorphism group of a tree . Journal of Combinatorial Theory, Series B 22 : 10 – 25 .
  • Zhang , C. , Fang , X. ( 2010 ). A note on the automorphism groups of cubic Cayley graphs of finite simple groups . Discrete Mathematics 310 : 3030 – 3032 .
  • Zelinka , B. ( 1981 ). Graphs of semigroups . Casopis. Pest. Mat. 106 : 407 – 408 .
  • Communicated by M. Bresar.

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