Automorphism Groups of Bouwer Graphs

作者：Zhang, Mimi; Zhou, Jinxin^*

来源：Algebra Colloquium, 2018, 25(3): 493-508.

DOI：10.1142/S1005386718000330

• Bouwer graph
• Cayley graph
• automorphism
• half-arc-transitive

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) vertical bar a is an element of Z(m), b is an element of
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} and two vertices being adjacent if they can be written as (a, b) and (a + 1, c), where either c = b or c = (c(1), c(2),...,c(k-1)) differs from b = (b(1), b(2),..., b(k)(-1)) in exactly one position, say the jth position, where c(j) = b(j) + 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.

• 出版日期2018-9
• 单位北京交通大学