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<p>A graph is said to be <i>edge-primitive</i> if it admits a group of automorphisms that acts primitively on its edge set. The study of edge-primitive graphs often involves examining such graphs with almost simple groups of automorphisms. Primitive groups of degree a product of three primes encompass a wide range of almost simple primitive groups. In this work, we classified edge-primitive graphs of order a product of three primes. The resulting graphs include two infinite families of edge-primitive graphs which are not 2-arc-transitive.</p>

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Edge-primitive graphs of order a product of three primes

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Ci Xuan Wu,
  • Fu-Gang Yin,
  • Zifeng Lai

摘要

A graph is said to be edge-primitive if it admits a group of automorphisms that acts primitively on its edge set. The study of edge-primitive graphs often involves examining such graphs with almost simple groups of automorphisms. Primitive groups of degree a product of three primes encompass a wide range of almost simple primitive groups. In this work, we classified edge-primitive graphs of order a product of three primes. The resulting graphs include two infinite families of edge-primitive graphs which are not 2-arc-transitive.