Automorphism groups of some generalized Cayley graphs

  • Mohsen Alinejad
  • Kazem KhashyarmaneshEmail author


Let R be a commutative ring with identity element. Graph \(\Gamma ^{n}_{R}\) is defined with vertex set \(R^{n} \setminus \lbrace 0 \rbrace \) and two distinct vertices X and Y are adjacent if and only if there exists an \(n \times n\) lower triangular matrix A with non-zero diagonal entries such that \(AX^T=Y^T\) or \(AY^T=X^T\). By \(B^{T}\), we mean transpose of matrix B. If R is a semigroup with respect to multiplication and \(n=1,\) then \(\Gamma ^{1}_{R}\) is the undirected Cayley graph. In this paper, a prime number p, we find the clique number and automorphism group of \(\Gamma ^{n}_{R},\) where \(R=\mathbb {Z}_{p^2}\) or \(R=\mathbb {Z}_{p^3}\).


Automorphism group Clique number Cayley graph 

Mathematics Subject Classification

Primary 05C69 05C75 13A15 



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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsFerdowsi University of MashhadMashhadIran

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