Journal article

Afflne flag graphs and classification of a family of symmetric graphs with complete quotients

Yu Qing Chen, Teng Fang, Sanming Zhou

DISCRETE MATHEMATICS | ELSEVIER | Published : 2019

Abstract

A graph Γ is G-symmetric if G is a group of automorphisms of Γ which is transitive on the set of ordered pairs of adjacent vertices of Γ. If V(Γ) admits a nontrivial G-invariant partition B such that for blocks B,C∈B adjacent in the quotient graph Γ B of Γ relative to B, exactly one vertex of B has no neighbour in C, then Γ is called an almost multicover of Γ B . In this case an incidence structure with point set B arises naturally, and it is a (G,2)-point-transitive and G-block-transitive 2-design if in addition Γ B is a complete graph. In this paper we classify all G-symmetric graphs Γ such that (i) B has block size |B|≥3; (ii) Γ B is complete and almost multi-covered by Γ; (iii) the incid..

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University of Melbourne Researchers

Grants

Awarded by China Postdoctoral Science Foundation


Awarded by Australian Research Council


Funding Acknowledgements

The authors would like to thank the anonymous referees for their comments which led to improvements of presentation. The second author was supported by China Postdoctoral Science Foundation Grant 2017M621065. The third author was supported by a Future Fellowship (FF110100629) of the Australian Research Council.