On the distance-transitivity of the folded hypercube

Document Type : Original paper

Author

Department of Mathematics, Faculty of Basic Science, Lorestan University, Khorramabad, Iran

Abstract

The folded hypercube FQn is the Cayley graph Cay(Z2n,S), where S={e1,e2,…,en}∪{u=e1+e2+⋯+en}, and ei=(0,…,0,1,0, …,0), with 1 at the ith position, 1≤i≤n. In this paper, we show that the folded hypercube FQn is a distance-transitive graph. Then, we study some properties of this graph. In particular, we show that if n≥4 is an even integer, then the folded hypercube FQn is an automorphic graph, that is, FQn is a distance-transitive primitive graph which is not a complete or a line graph.

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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 1
March 2025
Pages 207-217

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