Two-geodesic transitive graphs of order a product of two primes

Abstract

In a non-complete graph Γ, a vertex triple (u,v,w) with v adjacent to both u and w is called a 2- geodesic if u ≠ w and u, w are not adjacent. The graph Γ is said to be 2-geodesic transitive if its automorphism group is transitive on the set of arcs, and also transitive on the set of 2-geodesics. We first classify the family of 2- geodesic transitive graphs of order a product of two primes. Then, we determine exactly such graphs of valency 4. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.