Classifying cubic symmetric graphs of order 88p and 88p 2

Abstract

For a simple graph Γ\Gamma , Γ\Gamma is said to be ss-regular, provided that the automorphism group of Γ\Gamma regularly acts on the set consisting of ss-arcs of Γ\Gamma . Given a positive integer nn, the question on finding all ss-regular graphs of order nn and degree 3 has received considerable attention. An ss-regular graph with degree 3 is so-called a cubic symmetric graph. Let pp be a prime. We show that if Γ\Gamma is a cubic symmetric graph of order 88p88p, then p∈{5,11,23}p\in \left\{5,11,23\right\}; if Γ\Gamma is a cubic symmetric graph of order 88p288{p}^{2}, then p=11p=11. Moreover, we classify all cubic symmetric graphs of order 88p88p and 88p288{p}^{2}.

Keywords

• cubic symmetric graph
• simple group
• simple group
• 05c25