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On the symmetries of some classes of recursive circulant graphs | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 3، شماره 1، خرداد 2014، صفحه 1-6 اصل مقاله (502.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.3818 | ||
| نویسنده | ||
| Seyed Morteza Mirafzal* | ||
| Lorestan University | ||
| چکیده | ||
| 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 $2^{m+1}$. | ||
| کلیدواژه‌ها | ||
| Cayley graph؛ Recursive circulant؛ automorphism group؛ Dihedral group | ||
| مراجع | ||
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\href{http://arxiv.org/abs/1303.5974v2}{http://arxiv.org/abs/1303.5974v2}
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S. M. Mirafzal On the automorphism groups of regular hyper-stars and folded hyper-stars Ars Combinatoria (in press)
S. M. Mirafzal Some other algebraic properties of folded hypercubes Ars Combinatoria (in press)
J. H. Park and K. Y. Chwa (2000) Fundamental study recursive circulants and their embedding among hypercubes Theoret. Comput. Sci. 244, 35-62
J. J. Rotman (1995) An Introduction to the Theory of Groups 4th ed., Springer-Verlag, New York 148
J. X. Zhou (2011) The automorphism group of the alternating group graph Appl. Math. Lett. 24 (2), 229-231
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