Some algebraic properties of bipartite Kneser graphs

2018/04/12 by S. Morteza Mirafzal, Mirafzal, S. Morteza, Ali Zafari +1 · 1 citation
Engineering · Mathematics · #05C25 #94C15 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1804.04570

openalex publication_date 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let n and k be integers with n> k≥1 and [n] = \1, 2, ... , n\ . The bipartite Kneser graph H(n, k) is the graph with the all k-element and all (n-k)-element subsets of [n] as vertices, and there is an edge between any two vertices, when one is a subset of the other. In this paper, we show that H(n, k) is an arc-transitive graph. Also, we show that H(n,1) is a distance-transitive Cayley graph. Finally, we determine the automorphism group of the graph H(n, 1) and show that Aut(H(n, 1)) ≅ Sym([n] ) × ℤ₂, where ℤ₂ is the cyclic group of order 2. Moreover, we pose some open problems about the automorphism group of the bipartite Kneser graph H(n, k).

Citations

• A note on the automorphism groups of Johnson graphs

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