Vertex-transitive closures of graphs

Martin Bachratý; Grahame Erskine; Štefánia Glevitzká; Jozef Širáň; James Tuite

Vertex-transitive closures of graphs

Combinatorics 2026-07-10 v1

Authors: Martin Bachratý , Grahame Erskine , Štefánia Glevitzká , Jozef Širáň , James Tuite

Abstract

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

Cite

@article{arxiv.2607.09283,
  title  = {Vertex-transitive closures of graphs},
  author = {Martin Bachratý and Grahame Erskine and Štefánia Glevitzká and Jozef Širáň and James Tuite},
  journal= {arXiv preprint arXiv:2607.09283},
  year   = {2026}
}

Comments

8 pages, 3 figures