Finite hexavalent edge-primitive graphs

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August undefined, 2024

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 … Webedges. Weiss (in J. Comb. Theory Ser. B 15, 269–288, 1973) determined edge-primitive cubic graphs. In this paper, we classify edge-primitive pentavalent graphs. The same …

Vertex-primitive half-transitive graphs - Cambridge Core

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 … WebAug 1, 2024 · The finite edge-primitive pentavalent graphs Song-Tao Guo, Yan-Quan Feng, Caiheng Li Mathematics 2013 A graph is edge-primitive if its automorphism group acts primitively on edges. Weiss (in J. Comb. Theory Ser. B 15, 269–288, 1973) determined edge-primitive cubic graphs. In this paper, we classify… Expand 13 PDF golf tech michigan

Finite hexavalent edge-primitive graphs - ScienceDirect

WebFinite hexavalent edge-primitive graphs. Appl. Math. Comput. 378: 125207 (2024) 2010 – 2024. see FAQ. What is the meaning of the colors in the publication lists? 2024 [j22] ... On edge-primitive graphs of order twice a prime power. Discret. Math. 342 (12) (2024) [j20] view. electronic edition via DOI; WebTheorem 1.1. Let Γ be a connected nontrivial G-edge-primitive graph.Then Γ is G- arc-transitive, and one of the following holds. 1. Γ is G-vertex-primitive. 2. Γ is G-vertex-biprimitive. 3. Γ is a spread of a G-edge-primitive graph which is G-locally imprimitive. Conversely, a G-edge-primitive, G-locally imprimitive graph Σ is a quotient graph of a … WebNov 30, 2012 · A graph is edge-primitive if its automorphism group acts primitively on edges. Weiss (in J. Comb. Theory Ser. B 15, 269–288, 1973) determined edge … golf tech ltd

Finite edge-primitive graphs of prime valency Semantic Scholar

WebLet Γ be a finite connected undirected vertex transitive locally primitive graph of prime-power order. It is shown that either Γ is a normal Cayley graph of a 2-group, or Γ is a normal cover of a complete graph, a complete bipartite graph, or Σ ×l, where Σ= Kpm with p prime or Σ is the Schläfli graph (of order 27). WebFinite hexavalent edge-primitive graphs. Ci Xuan Wu, Jiangmin Pan. Finite hexavalent edge-primitive graphs. Applied Mathematics and Computation, 378: 125207, 2024. healthcare cmcWebMay 9, 2006 · Our theory is built on analysing several special classes of Cayley graphs (de-ﬁned in Subsection1.1), and analysing some operations on general Cayley graphs (discussed in Subsection1.2). 1.1. Basic edge-transitive Cayley graphs. For two groups X and Y,denote by X Y a semidirect product of X by Y,andbyX Y the central product of X … healthcare cme

"WebWeiss (1973) determined all cubic edge-primitive graphs, and Guo, Feng and Li recently determined all tetravalent and pentavalent edge-primitive graphs (notice that their method is difficult to treat the bigger valency case because the edge stabilizers may be insoluble). In this paper, we study hexavalent edge-primitive graphs by using line graphs. " - Finite hexavalent edge-primitive graphs

Finite hexavalent edge-primitive graphs

Applied Mathematics and Computation Vol 378, 1 August …

Webstudying how primitive elements lift to a given nite, regular cover. Here we consider free groups as fundamental groups of graphs. We will de ne primitive homology Hprim 1 (Y;C) in Subsection 4.4 as the subrepresentation of the homology of the cover that comes from primitive elements in the original space. Web5 Finite edge-primitive s-arc-transitive graphs with s 4 66 ... Here a graph is called edge-primitive if its automorphism group Aut acts primi-tively on the set of the edges. For edge-primitive s-arc-transitive graphs, where s 4, it is known that the stabilizers of their edges are soluble (see [38,126]). Therefore to

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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. WebThen there exists a G-basic, G-locally-primitive graph of valency p satisfying Theorem 1.5(b) (ii) with M1 ∼= M2 ∼= T. (See Proposition 2.2 for the construction and proof.) A natural problem arising from these results is the problem of constructing nite locally-quasiprimitive graphs as multicovers of a given locally-quasiprimitive graph.

WebApr 9, 2009 · Given an infinite family of finite primitive groups, conditions are found which ensure that almost all the orbitals are not self-paired. If p is a prime number congruent to ±1(mod 10), these conditions apply to the groups P S L (2, p) acting on the cosets of a subgroup isomorphic to A 5.In this way, infinitely many vertex-primitive ½-transitive … WebThe study of edge-primitive graphs was reinvigorated in 2010 by the first author and Li [8] by providing a general structure theorem of such graphs and classifying all edge-primitive...

WebJun 1, 2024 · In this paper, we classify hexavalent half-arc-transitive graphs of order 9 p for each prime p. As a result, there are four infinite families of such graphs: three defined on Z p ⋊ Z 27 with 27 ( p − 1); one defined on Z 3 p ⋊ Z 9 with 9 ( p − 1). Half-arc-transitive graph Edge-transitive graph Arc-transitive graph Cayley graph Coset graph 1. WebFeb 28, 2011 · This paper gives an explicit list of the soluble maximal subgroups of almost simple groups. The classification is then applied to classify edge-primitive s-arc …

WebAug 1, 2024 · In this paper, we study hexavalent edge-primitive graphs by using line graphs. The s-arc-transitivity of such graphs are determined, and the automorphism …

WebMathematical methods of diagonalization of quadratic forms applied to the study of stability of thermodynamic systems. F.N. Lima, J.M. De Sousa. Article 125176. View PDF. Article preview. healthcare cluster in singaporeWebAug 1, 2024 · Finite hexavalent edge-primitive graphs☆ Preliminary results. We begin with an observation regarding the vertex stabilizers (also their Sylow 2-subgroups) and... … golf tech marylandWebSep 14, 2009 · Many famous graphs are edge-primitive, for example, the Heawood graph, the Tutte--Coxeter graph and the Higman--Sims graph. In this paper we systematically … golf tech milwaukeeWebOct 1, 2024 · A graph is edge-primitive if its automorphism group acts primitively on the edge set. In this short paper, we prove that a finite 2-arc-transitive edge-primitive graph has almost simple automorphism… 2 PDF References SHOWING 1-10 OF 24 REFERENCES SORT BY On finite edge-primitive and edge-quasiprimitive graphs … healthcare cmiWebIn 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 … golf tech logoWebOct 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. healthcare cmgWebAug 1, 2024 · Finite hexavalent edge-primitive graphs☆ 1. Introduction. For a finite and undirected graph Γ, the expression denotes the group of all of its automorphisms. If... 2. … golf tech longmont