Let k, m and n be three positive integers such that 2^m= 1 （mod n） and k ≥ 2. The Bouwer graph, which is denoted by B（k,m,n）, is the graph with vertex set {（a,b） ｜ a ∈Zm, b ∈Zn×…×Zn} k-1 times and...Let k, m and n be three positive integers such that 2^m= 1 （mod n） and k ≥ 2. The Bouwer graph, which is denoted by B（k,m,n）, is the graph with vertex set {（a,b） ｜ a ∈Zm, b ∈Zn×…×Zn} k-1 times and two vertices being adjacent if they can be written as （a,b） and （a＋ 1,c）, where either c ： b or c = （cl,c2 …,ck-1） differs from b = （b1, b2,…, bk-1） in exactly one position, say the jth position, where cj = bj ＋ 2^a. Every B（k, m, n） is a vertex- and edge-transitive graph, and Bouwer proved that B（k, 6, 9） is half-arc-transitive for every k ≥ 2. In 2016, Conder and Zitnik gave the classification of half-arc-transitive Bouwer graphs. In this paper, the full automorphism group of every B（k, m, n） is determined.展开更多
基金This work was partially supported by the National Natural Science Foundation of China （11671030） and the Fundamental Research Funds for the Central Universities （2015JBM110）.
文摘Let k, m and n be three positive integers such that 2^m= 1 （mod n） and k ≥ 2. The Bouwer graph, which is denoted by B（k,m,n）, is the graph with vertex set {（a,b） ｜ a ∈Zm, b ∈Zn×…×Zn} k-1 times and two vertices being adjacent if they can be written as （a,b） and （a＋ 1,c）, where either c ： b or c = （cl,c2 …,ck-1） differs from b = （b1, b2,…, bk-1） in exactly one position, say the jth position, where cj = bj ＋ 2^a. Every B（k, m, n） is a vertex- and edge-transitive graph, and Bouwer proved that B（k, 6, 9） is half-arc-transitive for every k ≥ 2. In 2016, Conder and Zitnik gave the classification of half-arc-transitive Bouwer graphs. In this paper, the full automorphism group of every B（k, m, n） is determined.
