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摘要
A graph X, with a group G of automorphisms of X, is said to be (G, s)-transitive, for some s >= 1, if G is transitive on s-arcs but not on (s + 1)-arcs. Let X be a connected (G, s)-transitive graph of prime valency p >= 5, and G(upsilon) the vertex stabilizer of a vertex upsilon is an element of V (X). Suppose that G(upsilon) is solvable. Weiss (1974) proved that |G(upsilon)vertical bar vertical bar p(p - 1)(2). In this paper, we prove that G(upsilon) congruent to (L-p x L-m) x L-n for some positive integers m and n such that n vertical bar m and m vertical bar p - 1.
- 出版日期2015-9
- 单位河南大学
