Vertex-transitivity on folded crossed cubes

• The vertex-transitive property is advantageous to the design and simulation of some algorithms in graphs.
• We study the vertex-transitivity on folded crossed cubes FCQnFCQn.
• We prove that FCQnFCQn is vertex-transitivity if and only if n∈{1,2,4}n∈{1,2,4}.

Kulasinghe and Bettayeb (1995) [11] proved that the crossed cube CQnCQn (a synonym called multiply-twisted hypercube in that paper) fails to be vertex-transitive for n⩾5n⩾5. In this paper, we study vertex-transitivity on folded crossed cubes FCQnFCQn and show that FCQnFCQn is vertex-transitive if and only if n∈{1,2,4}n∈{1,2,4}. In particular, we also enumerate all automorphisms when n=4n=4.