Classifying cubic symmetric graphs of order 88p and 88p 2 - Zhai Liangliang (Open Mathematics)
For a simple graph ΓΓ , ΓΓ is said to be ss-regular, provided that the automorphism group of ΓΓ regularly acts on the set consisting of ss-arcs of ΓΓ . 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 ΓΓ is a cubic symmetric graph of order 88p88p, then p∈{5,11,23}p\in \left\{5,11,23\right\}; if ΓΓ 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}.