# On the symmetries of some classes of recursive circulant graphs

Document Type: Research Paper

Author

Lorestan University

Abstract

A recursive-circulant $G(n; d)$ is defined to be a‎ ‎circulant graph with $n$ vertices and jumps of powers of $d$‎.
‎$G(n; d)$ is vertex-transitive‎, ‎and has some strong hamiltonian‎ ‎properties‎. ‎$G(n;d)$ has a recursive structure when $n = cd^m$‎, ‎$1 \leq c < d$ [Theoret‎. ‎Comput‎. ‎Sci. 244 (2000) 35-62]‎. ‎In this paper‎, ‎we will find the automorphism‎ ‎group of some classes of recursive-circulant graphs‎. ‎In particular‎, ‎we‎ ‎will find that the automorphism group of $G(2^m; 4)$ is isomorphic‎ ‎with the group $D_{2 \cdot 2^m}$‎, ‎the dihedral group of order $2^{m+1}$‎.

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