High-girth arc-transitive graphs

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Web1 de mai. de 1989 · Highly Arc Transitive Digraphs. Finite digrahs Г with a group G of automorphisms acting transitively on the set of s -arcs, for some s ⩾ 2, are investigated. For each valency v and each s ⩾ 2 an infinite family of finite digraphs of valency v which are s -arc transitive but not ( s + 1)-arc transitive are constructed. Web1 de mar. de 2001 · It is proved that if Γ is a finite connected s-transitive graph (where s≥ 2) of order a p-power with pprime, then s= 2 or 3; further, either s= 3 and Γ is a normal cover of the complete bipartite graph K2m,2m, or s= 2 and Γ is a normal cover of one of the following 2-transitive graphs: Kpm+1(the complete graph of order pm+ 1), …

Affine extensions of the Petersen graph and 2‑arc‑transitive …

WebA. A. Ivanov [4] found a relationship between 2-arc-transitive graphs of girth 5 and flag-transitive geometries with the diagram P L O 0 0 In particular, such a geometry can … WebIf a graph Γ is (G,s)-arc transitive and s ≤ diam(Γ), then s-geodesics and s-arcs are same, and Γ is (G,s)-geodesic transitive. However, Γ can be (G,s)-geodesic transitive but not … greek hats for women

arXiv:1908.09361v4 [math.CO] 7 Nov 2024

Web4 de mai. de 2024 · In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth $6$ is obtained. It is proved that every such graph, with the exception of the Desargues graph on ... Web1 de abr. de 2007 · In this section, we will find out all connected 5-arc transitive cubic Cayley graphs for A 47. We first denote each coset G a ∈ Ω = [ A: G] by a ¯. Then Ω = T ¯ ≔ { h ¯ ∣ h ∈ T } and G is the point stabilizer of 1 ¯ in A. For any subgroup L of T and its left coset h L, the set h L ¯ is obviously an L -orbit in Ω. Webinitial 3-arc will not be equivalent under any automorphism. 13(*). Let G be a distance transitive graph with girth at least five. Let k = 1. Then G is at least k-arc transitive. Consider any two k+1-arcs (they may be taken to start from the same vertex x because G is vertex-transitive). If they have an edge in common, then k-arc greek healthcare system

A characterisation on arc-transitive graphs of prime valency

ARC–TRANSITIVE NON–CAYLEY - EMIS

WebAn arc in a graph is an ordered pair of adjacent vertices, and so a graph is arc-transitive if its automorphism group acts transitively on the set of arcs. As we have seen, this is a … Web9 de abr. de 2024 · When the underlying graphs exhibit a significant girth and expanding factor, ... Then they are called edge-transitive Cayley graphs such that Lemma 4 of is satisfied ... Chou, P.-C., & Ueng, Y.-L. (2024). An effective low-complexity error-floor lowering technique for high-rate QC-LDPC codes. IEEE Communications Letters, 22(10 ... flow diagram creatorWebIn this section, we construct an inﬁnite family ofG-arc-transitive graphs such thatG is biquasiprimitive on vertices butG+is not quasiprimitive on each bipartite half. Construction 3.1Let H=Zp×Zp×Z2where p≡1(mod 3) is a prime. Let a be an element of multiplicative order3inZp. We deﬁne a graph with vertex-set H and edges of the form greek health ministry

"WebThe graph Σ is called (G, 2)-arc transitive, where G ≤ Aut(Σ), if G is transitive on the vertex set and on the set of 2-arcs of Σ. From a previous study it arises the question of when a … " - High-girth arc-transitive graphs

High-girth arc-transitive graphs

Cubic s-arc transitive Cayley graphs - ScienceDirect

WebLet G be a finite non-abelian simple group and let Γ be a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal in the … Web1 de ago. de 2010 · A near-polygonal graph is a graph Γ which has a set C of m-cycles for some positive integer m such that each 2-path of Γ is contained in exactly one cycle in C. …

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Webacts 2-arc-transitively on the quotient graph X. By Proposition 1.1, the class of ﬁnite connected 2-arc-transitive graphs can be divided into two subclasses as follows: (1) The 2-arc-transitive graphs Xwith the property that either (i) every nontrivial normal subgroup of Aut Xacts transitively on V(X),or (ii) every nontrivial normal subgroup WebArc-transitivity is an even stronger property than edge-transitivity or vertex-transitivity, so arc-transitive graphs have a very high degree of symmetry. A 0-transitive graph is …

WebA new approach to catalog small graphs of high even girth Vivek S. Nittoor [email protected] Independent Consultant & Researcher (formerly with the University of Tokyo) Abstract A catalog of a class of (3;g) graphs for even girth gis introduced in this pa-per. A (k;g) graph is a regular graph with degree kand girth g. This catalog of WebClearly λ k ≤ d k − e k, where d is the degree of Γ and e k is the maximal number of edges induced on a set of k vertices. We shall show that Cayley graphs with a prime order and …

WebARC–TRANSITIVE NON–CAYLEY GRAPHS FROM REGULAR MAPS P. GVOZDJAK and J. ˇSIR A´Nˇ Abstract. We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r≥3 and pis a prime greater than r(r−1). 1. Introduction Orientable maps, i.e., embeddings of graphs in orientable surfaces ... Weba high level of symmetry. For example, arc-transitive 4-valent graphs of girth at most 4 were characterised in [29]. In the case of cubic graphs, even more work has been done. The structure of cubic arc-transitive graphs of girth at most 7 and 9 was studied in [12] and [7], respectively, and those of girth 6 were completely determined in [22].

WebThe study of cubic s-arc-transitive graphs goes back to the seminal papers of Tutte [14, 15] who showed that s ≤ 5. More generally, Weiss [16] proved that s ≤ 7for graphs of …

WebAn arc in a graph is an ordered pair of adjacent vertices, and so a graph is arc-transitive if its automorphism group acts transitively on the set of arcs. As we have seen, this is a stronger property than being either vertex transitive or edge transitive, and so we can say even more about arc-transitive graphs. flow diagram design onlineWeb3 de out. de 2006 · In fact we will show that every 5-arc-transitive cubic Cayley graph Cay (G, S) is a cover of one of just six such graphs, which are the only examples with G core-free in Aut Cay (G, S). The... flow diagram chart in algebraWeb28 de out. de 2009 · An arc-transitive graph Γ is said to be (X, s)-regular if it is (X, s)-arc-transitive and, for any two s-arcs of Γ, there is a unique automorphism of Γ mapping one … flow diagram basicsWeb16 de dez. de 2010 · A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex-transitive graphs of a given degree and girth 6 and relate their constructions to near-difference sets. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:265-284, 2011 greek health spa where nothing is forbiddenWebWe prove the existence of vertex transitive trivalent graphs of arbitrarily high girth using Cayley graphs. The same result is proved for symmetric (that is vertex transitive and … flow diagram consort 2010Web25 de ago. de 2003 · ANALYSING FINITE LOCALLYs-ARC TRANSITIVE GRAPHS. MICHAEL GIUDICI, CAI HENG LI, AND CHERYL E. PRAEGER Abstract. We present a … flow diagram draw ioWeb1 de mar. de 2024 · The main result of this paper states that with the exception of a single graph, the famous Desargues graph on 20 vertices (that can also be defined as the … greek health system