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(2004)
Shift automorphisms of nite order
(2011)
Shift automorphisms of nite outer order
V. Mazurov (1991)
Finite groups of outer automorphisms of free groupsSiberian Mathematical Journal, 32
J. Munkres (1984)
Elements of algebraic topology
Abstract A finite symmetric graph Γ is a pair ( Γ , f ) $(\Gamma ,f)$ , where Γ is a finite graph and f : Γ → Γ $f:\Gamma \rightarrow \Gamma $ is a graph self equivalence or automorphism. We develop several tools for studying such symmetries. In particular, we describe in detail all symmetries with a single edge orbit, we prove that each symmetric graph has a maximal forest that meets each edge orbit in a sequential set of edges – a sequential maximal forest – and we calculate the characteristic polynomial χ f ( t ) $\chi _f(t)$ and the minimal polynomial μ f ( t ) $\mu _f(t)$ of the linear map H 1 ( f ) : H 1 ( Γ , ℤ ) → H 1 ( Γ , ℤ ) $H_1(f):H_1(\Gamma ,\mathbb {Z})\rightarrow H_1(\Gamma ,\mathbb {Z})$ . The calculation is in terms of the quotient graph Γ ¯ $\overline{\Gamma }$ .
Groups Complexity Cryptology – de Gruyter
Published: May 1, 2015
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