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NEW CONSTRUCTIONS OF SELF-COMPLEMENTARY CAYLEY GRAPHS

Part of: Permutation groups Graph theory

Published online by Cambridge University Press:  12 January 2021

CAI HENG LI ,
GUANG RAO  and
SHU JIAO SONG Open the ORCID record for SHU JIAO SONG [Opens in a new window]
CAI HENG LI
Affiliation:
Southern University of Science and Technology, Shenzhen, China e-mail: lich@sustc.edu.cn
GUANG RAO
Affiliation:
The Chinese University of Hong Kong, Shenzhen, China e-mail: raoguang@cuhk.edu.cn
SHU JIAO SONG
Affiliation:
Yantai University, Yantai, China e-mail: shujiao.song@ytu.edu.com
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Abstract

Vertex-primitive self-complementary graphs were proved to be affine or in product action by Guralnick et al. [‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc.356 (2004), 4857–4872]. The product action type is known in some sense. In this paper, we provide a generic construction for the affine case and several families of new self-complementary Cayley graphs are constructed.

Keywords

Cayley graphmetacirculant graphself-complementary graph

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Secondary: 20B05: General theory for finite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 111 , Issue 3 , December 2021 , pp. 372 - 385
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Michael Giudici

This work was partially supported by NSFC (Nos. 61771019, 11701497 and 11771200) and NSFS (No. ZR2017MA022).

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