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arXiv · 2607.09283

Vertex-transitive closures of graphs

Martin Bachratý·Grahame Erskine·Štefánia Glevitzká·Jozef Širáň·James Tuite
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Abstract

A vertex-transitive closure of $Γ$ is a vertex-transitive supergraph of $Γ$ on the same vertex set. The vertex-transitive number of a graph $Γ$, denoted by $d_{vt}(Γ)$, is the smallest integer for which there exists a $d_{vt}(Γ)$-regular vertex-transitive closure of $Γ$. In this paper we use various algebraic and combinatorial methods to study vertex-transitive closures of graphs and the associated vertex-transitive number.

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Martin Bachratý, Grahame Erskine, Štefánia Glevitzká, Jozef Širáň, James Tuite. 2026-07-10. Vertex-transitive closures of graphs. https://arxiv.org/abs/2607.09283

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