Article

# Automorphisms of cubic Cayley graphs of order 2pq.

• ##### Yan-Quan Feng
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China
Discrete Mathematics 01/2009; 309:2687-2695. DOI: 10.1016/j.disc.2008.06.023
Source: DBLP

ABSTRACT In this paper the automorphism groups of connected cubic Cayley graphs of order 2pq for distinct odd primes p and q are determined. As an application, all connected cubic non-symmetric Cayley graphs of order 2pq are classified and this, together with classifications of connected cubic symmetric graphs and vertex-transitive non-Cayley graphs of order 2pq given by the last two authors, completes a classification of connected cubic vertex-transitive graphs of order 2pq.

0 Bookmarks
·
77 Views
• Source
##### Article: Automorphism Group of the Derangement Graph.
Electr. J. Comb. 01/2011; 18.
• Source
##### Article: Maximum-Size Independent Sets and Automorphism Groups of Tensor Powers of the Even Derangement Graphs
[Hide abstract]
ABSTRACT: Let $A_n$ be the alternating group of even permutations of $X:=\{1,2,...,n\}$ and ${\mathcal E}_n$ the set of even derangements on $X.$ Denote by $A\T_n^q$ the tensor product of $q$ copies of $A\T_n,$ where the Cayley graph $A\T_n:=\T(A_n,{\mathcal E}_n)$ is called the even derangement graph. In this paper, we intensively investigate the properties of $A\T_n^q$ including connectedness, diameter, independence number, clique number, chromatic number and the maximum-size independent sets of $A\T_n^q.$ By using the result on the maximum-size independent sets $A\T_n^q$, we completely determine the full automorphism groups of $A\T_n^q.$
11/2011;
• ##### Article: On cubic non-Cayley vertex-transitive graphs.
[Hide abstract]
ABSTRACT: In 1983, the second author [D. Marušič, Ars Combinatoria 16B (1983), 297–302] asked for which positive integers n there exists a non-Cayley vertex-transitive graph on n vertices. (The term non-Cayley numbers has later been given to such integers.) Motivated by this problem, Feng [Discrete Math 248 (2002), 265–269] asked to determine the smallest valency ϑ(n) among valencies of non-Cayley vertex-transitive graphs of order n. As cycles are clearly Cayley graphs, ϑ(n)⩾3 for any non-Cayley number n.In this paper a goal is set to determine those non-Cayley numbers n for which ϑ(n) = 3, and among the latter to determine those for which the generalized Petersen graphs are the only non-Cayley vertex-transitive graphs of order n. It is known that for a prime p every vertex-transitive graph of order p, p2 or p3 is a Cayley graph, and that, with the exception of the Coxeter graph, every cubic non-Cayley vertex-transitive graph of order 2p, 4p or 2p2 is a generalized Petersen graph. In this paper the next natural step is taken by proving that every cubic non-Cayley vertex-transitive graph of order 4p2, p>7 a prime, is a generalized Petersen graph. In addition, cubic non-Cayley vertex-transitive graphs of order 2pk, where p>7 is a prime and k⩽p, are characterized. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 77–95, 2012
Journal of Graph Theory 01/2012; 69:77-95. · 0.63 Impact Factor