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arXiv · 2104.02325

General Form of the Automorphism Group of Bicyclic Graphs

Somayeh Madani·Ali Reza Ashrafi
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Abstract

In 1869, Jordan proved that the set $\mathcal{T}$ of all finite group that can be represented as the automorphism group of a tree is containing the trivial group and it is closed under taken direct product of groups of lower order in $\mathcal{T}$ and wreath product of a member in $\mathcal{T}$ and the symmetric group on $n$ symbols. The aim of this paper is to continue this work and another works by Klav$\acute{\rm i}$k and Zeman in 2017 to present a class $\mathcal{S}$ of finite groups for which the automorphism group of each bicyclic graph is a member of $\mathcal{S}$ and this class is minimal with this property.

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Somayeh Madani, Ali Reza Ashrafi. 2021-04-06. General Form of the Automorphism Group of Bicyclic Graphs. https://arxiv.org/abs/2104.02325

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