Show Summary Details
More options …

# Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2018: 0.38

Online
ISSN
1869-6104
See all formats and pricing
More options …
Volume 7, Issue 1

# Symmetries of finite graphs and homology

Benjamin Atchison
/ Edward C. Turner
Published Online: 2015-04-14 | DOI: https://doi.org/10.1515/gcc-2015-0003

## Abstract

A finite symmetric graph Γ is a pair $\left(\Gamma ,f\right)$, where Γ is a finite graph and $f:\Gamma \to \Gamma$ 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 ${\chi }_{f}\left(t\right)$ and the minimal polynomial ${\mu }_{f}\left(t\right)$ of the linear map ${H}_{1}\left(f\right):{H}_{1}\left(\Gamma ,ℤ\right)\to {H}_{1}\left(\Gamma ,ℤ\right)$. The calculation is in terms of the quotient graph $\overline{\Gamma }$.

MSC: 20E05; 20F28; 05C20; 05C25; 05C50

Published Online: 2015-04-14

Published in Print: 2015-05-01

Funding Source: Framingham State University

Award identifier / Grant number: CELTSS

Citation Information: Groups Complexity Cryptology, Volume 7, Issue 1, Pages 11–30, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144,

Export Citation