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http://dx.doi.org/10.4134/BKMS.2015.52.4.1169

GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS  

ZHU, YONGWEN (SCHOOL OF MATHEMATICS AND INFORMATION SCIENCE YANTAI UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 1169-1183 More about this Journal
Abstract
We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.
Keywords
generalized Cayley graph of semigroups; rectangular group; connected graph; isomorphism; colour-preserving automorphism; vertex-transitive;
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1 L. Babai, Automorphism groups, isomorphism, reconstruction, in: Handbook of Combinatorics, pp. 1447-1540, Elsevier, Amsterdam, 1995.
2 A. Devillers, W. Jin, C. H. Li, and C. E. Praeger, On normal 2-geodesic transitive Cayley graphs, J. Algebraic Combin. 39 (2014), no. 4, 903-918.   DOI   ScienceOn
3 S. Fan, Vertex transitive Cayley graphs of semigroups of order a product of two primes, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 14 (2007), Bio-inspired computing theory and applications, Part 2, suppl. S3, pp. 905-909.
4 R. S. Gigon, Rectangular group congruences on a semigroup, Semigroup Forum 87 (2013), no. 1, 120-128.   DOI   ScienceOn
5 C. D. Godsil, On Cayley graph isomorphisms, Ars Combin. 15 (1983), 231-246.
6 D. Grynkiewicz, V. F. Lev, and O. Serra, Connectivity of addition Cayley graphs, J. Combin. Theory Ser. B 99 (2009), no. 1, 202-217.   DOI   ScienceOn
7 Y. Hao, X. Yang, and N. Jin, On transitive Cayley graphs of strong semilattices of rectangular groups, Ars Combin. 105 (2012), 183-192.
8 J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford, 1995.
9 A. V. Kelarev, On undirected Cayley graphs, Australas. J. Combin. 25 (2002), 73-78.
10 A. V. Kelarev, Graph Algebras and Automata, Marcel Dekker, Inc., New York, 2003.
11 A. V. Kelarev and C. E. Praeger, On transitive Cayley graphs of groups and semigroups, European J. Combin. 24 (2003), no. 1, 59-72.   DOI   ScienceOn
12 A. V. Kelarev and S. J. Quinn, Directed graphs and combinatorial properties of semigroups, J. Algebra 251 (2002), no. 1, 16-26.   DOI   ScienceOn
13 A. V. Kelarev, J. Ryan, and J. Yearwood, Cayley graphs as classifiers for data mining: The influence of asymmetries, Discrete Math. 309 (2009), no. 17, 5360-5369.   DOI   ScienceOn
14 B. Khosravi and M. Mahmoudi, On Cayley graphs of rectangular groups, Discrete Math. 310 (2010), no. 4, 804-811.   DOI   ScienceOn
15 C. H. Li, Finite CI-groups are soluble, Bull. London Math. Soc. 31 (1999), no. 4, 419-423.   DOI
16 C. H. Li, On isomorphisms of finite Cayley graphs-a survey, Discrete Math. 256 (2002), no. 1-2, 301-334.   DOI   ScienceOn
17 S. Panma, Characterization of Cayley graphs of rectangular groups, Thai J. Math. 8 (2010), no. 3, 535-543.
18 S. Panma, N. N. Chiangmai, U. Knauer, and Sr. Arworn, Characterizations of Clifford semigroup digraphs, Discrete Math. 306 (2006), no. 12, 1247-1252.   DOI   ScienceOn
19 S. Panma, U. Knauer, and Sr. Arworn, On transitive Cayley graphs of right (left) groups and of Clifford semigroups, Thai J. Math. 2 (2004), 183-195.
20 S. Panma, U. Knauer, and Sr. Arworn, On transitive Cayley graphs of strong semilattices of right (left) groups, Discrete Math. 309 (2009), no. 17, 5393-5403.   DOI   ScienceOn
21 M. Suzuki, Group Theory I, Springer, New York, 1982.
22 Y. Zhu, Generalized Cayley graphs of semigroups II, Semigroup Forum 84 (2012), no. 1, 144-156.   DOI
23 S. F. Wang, A problem on generalized Cayley graphs of semigroups, Semigroup Forum 86 (2013), no. 1, 221-223.   DOI
24 R. J. Wilson, Introduction to Graph Theory, 3rd edn, Longman, New York, 1982.
25 Y. Zhu, Generalized Cayley graphs of semigroups I, Semigroup Forum 84 (2012), no. 1, 131-143.   DOI
26 Y. Zhu, Cayley-symmetric semigroups, Bull. Korean Math. Soc. 52 (2015), no. 2, 409-419.   DOI   ScienceOn