Journal article

Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers

Binzhou Xia

JOURNAL OF COMBINATORIAL THEORY SERIES B | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2021

Abstract

Half-arc-transitive graphs are a fascinating topic which connects graph theory, Riemann surfaces and group theory. Although fruitful results have been obtained over the last half a century, it is still challenging to construct half-arc-transitive graphs with prescribed vertex stabilizers. Until recently, there have been only six known connected tetravalent half-arc-transitive graphs with nonabelian vertex stabilizers, and the question whether there exists a connected tetravalent half-arc-transitive graph with nonabelian vertex stabilizer of order 2s for every s⩾3 has been wide open. This question is answered in the affirmative in this paper via the construction of a connected tetravalent hal..

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University of Melbourne Researchers