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Constructing infinitely many half-arc-transitive covers of tetravalent graphs
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abstract
We prove that, given a finite graph $\Sigma$ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of $\Sigma$. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order $2^8$ of finite connected tetravalent half-arc-transitive graphs. This sheds some new light on the longstanding problem of classifying the vertex stabilizers of finite tetravalent half-arc-transitive graphs.
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Cited by 1 Pith paper
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Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers
For every integer m >= 1, there is a connected tetravalent half-arc-transitive graph with vertex stabilizer D8^2 x C2^m, built as a coset graph on the alternating group A_{2m+6}.
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