Article

# Automorphisms of cubic Cayley graphs of order

Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China
(Impact Factor: 0.56). 05/2009; 309(9):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.

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• "One difficult problem in Algebraic Graph Theory is to determine the automorphism groups of Cayley graphs. Although there are some nice results on the automorphism groups of Cayley graphs (see [6] [7] [8] [10] [13] [23] [24] [25] "
##### Article: Maximum-Size Independent Sets and Automorphism Groups of Tensor Powers of the Even Derangement Graphs
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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 $A\T_n^q.$
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• "Feng and Xu [7] determined the automorphism groups of tetravalent Cayley graphs on regular p-groups. Recently, Zhang et al. [22] determined the automorphism groups of cubic Cayley graphs of order 2pq. For other results on the automorphism groups of Cayley graphs, we refer the readers to [5] [6] [11] [12] [18] [20] [21]. "
##### Article: Automorphism Group of the Derangement Graph.
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ABSTRACT: We prove that the full automorphism group of the derangement graph Γ n (n≥3) is equal to (R(S n )⋊Inn(S n ))⋊Z 2 , where R(S n ) and Inn(S n ) are the right regular representation and the inner automorphism group of S n respectively, and Z 2 =〈φ〉 with the mapping φ:σ φ =σ -1 , ∀σ∈S n . Moreover, all orbits on the edge set of Γ n (n≥3) are determined.
The electronic journal of combinatorics 01/2011; 18. · 0.49 Impact Factor
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• "Let p and q be two primes. In [25] [26] [27], all connected cubic non-normal Cayley graphs of order 2pq are determined. Wang and Xu [23] determined all tetravalent non-normal 1- regular Cayley graphs on dihedral groups. "
##### Article: Tetravalent Non-Normal Cayley Graphs of Order 4p.
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ABSTRACT: A Cayley graph Cay(G, S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G, S). In this paper, all connected tetravalent non-normal Cayley graphs of order 4p are constructed explicitly for each prime p. As a result, there are fifteen sporadic and eleven infinite families of tetravalent non-normal Cayley graphs of order 4p.
The electronic journal of combinatorics 09/2009; 16(1). · 0.49 Impact Factor