WebJan 9, 2024 · It is known that finite non-bipartite locally primitive arc-transitive graphs are normal covers of ‘basic objects’—vertex quasiprimitive ones. Praeger in (J London Math Soc 47(2):227–239, 1993) showed that a quasiprimitive action of a group G on a nonbipartite finite 2-arc transitive graph must be one of four of the eight O’Nan–Scott types. In this … WebLi et al. [9] considered primitive half-arc-transitive graphs. C. Proposition 2.3 [9, Theorem 1.4] There are no vertex-primitive half-arc-transitive graphs of valency less than 10. The following proposition can be extracted from Theorem 2.4 and Table 1 in [10]. D. Proposition 2.4 . Let X be a connected edge-transitive graph of order 2p
Edge-Primitive Graphs of Prime Power Order SpringerLink
WebOct 14, 2011 · We characterise regular bipartite locally primitive graphs of order 2 p e, where p is prime. We show that either p =2 (this case is known by previous work), or the graph is a binormal Cayley graph or a normal cover of one of the basic locally primitive graphs; these are described in detail. WebOct 1, 2024 · Many famous graphs are edge-primitive. Weiss (1973) and Guo et al. (2013) determined edge-primitive graphs of valency 3 and 5, respectively. In this paper, we study edge-primitive graphs of any prime valency. sonicspeedtornado youtube channel
The finite edge-primitive pentavalent graphs - DeepDyve
WebJan 4, 2024 · A graph is called edge-primitive if its automorphism group acts primitively on its edge-set. In this paper, edge-primitive graphs of prime power order are determined. 1 Introduction Throughout the paper, graphs are assumed to be finite undirected graphs without loops and multiple edges. WebFeb 12, 2014 · Let X be a finite simple undirected graph with a subgroup G of the full automorphism group Aut(X). Then X is said to be (G, s)-transitive for a positive integer s, if G is transitive on s-arcs but not on (s + 1)-arcs, and s-transitive if it is (Aut(X), s)-transitive. Let G v be a stabilizer of a vertex v ∈ V (X) in G. Up to now, the structures of vertex … WebIn this paper, we study hexavalent edge-primitive graphs by using line graphs. The s-arc-transitivity of such graphs are determined, and the automorphism groups of such … sonic speed simulator tier list