Half-Transitive Graphs of Valency Twice a Prime

Zai-Ping Lu
Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, P. R. China


Abstract     Full Text  PDF

A graph is said to be half-transitive if its automorphism group acts transitively on the vertex set and edge set but intransitively on the arc set. In this paper, we construct infinitely many primitive half-transitive graphs with automorphism groups the symmetric groups of prime degrees, and show that there exists at least one primitive half-transitive graph of valency $2p$ for a prime $p$ no less than $7$ and $p\ne 13$. As a byproduct of our construction, infinitely many primitive $2$-arc-regular Cayley graphs are given.