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NOWHERE-ZERO $3$-FLOWS IN TWO FAMILIES OF VERTEX-TRANSITIVE GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  15 September 2022

JUNYANG ZHANG Open the ORCID record for JUNYANG ZHANG [Opens in a new window]  and
YING TAO Open the ORCID record for YING TAO [Opens in a new window]
JUNYANG ZHANG*
Affiliation:
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, PR China
YING TAO
Affiliation:
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, PR China e-mail: 2290682363@qq.com
*
e-mail: jyzhang@cqnu.edu.cn
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Abstract

Let $\Gamma $ be a graph of valency at least four whose automorphism group contains a minimally vertex-transitive subgroup G. It is proved that $\Gamma $ admits a nowhere-zero $3$ -flow if one of the following two conditions holds: (i) $\Gamma $ is of order twice an odd number and G contains a central involution; (ii) G is a direct product of a $2$ -subgroup and a subgroup of odd order.

Keywords

vertex-transitive graphinteger flownowhere-zero 3-flowCayley graph

MSC classification

Primary: 05C21: Flows in graphs
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 3 , June 2023 , pp. 353 - 360
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author was supported by the Basic Research and Frontier Exploration Project of Chongqing (No. cstc2018jcyjAX0010) and the Foundation of Chongqing Normal University (21XLB006).

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