2024 High-girth arc-transitive graphs

High-girth arc-transitive graphs

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WebA 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 (3;g) graphs for even girth gsatisfying 6 g 16, has the following properties. …

Cubic s-arc transitive Cayley graphs - ScienceDirect

Webconstructed half-arc-transitive graphs of valency 2k for all integers k > 2 (see also [12]). Note that a graph of valency 2 is a disjoint union of cycles and hence not half-arc-transitive. Thus the valency of a half-arc-transitive graph is at least 4. Over the last half a century, numerous papers have been published on half-arc- Web3 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... req recherche

Notes: A construction of an infinite family of 2-arc transitive ...

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 … 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), … 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 … propolis lozenges bee health

TETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED …

Algebraic Graph Theory - Mathematics

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 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 ... req.setheader is not a functionWebTETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED VERTEX-STABILIZERS PRIMOŽ POTOCNIK, PABLO SPIGAˇ and GABRIEL VERRET (Received … propolis natura foundation

"Web24 de dez. de 2014 · On -arc-transitive graphs of order. We show that there exist functions and such that, if , and are positive integers with and is a -valent -arc-transitive graph of order with a prime, then . In other words, there are only finitely many -valent 2-arc-transitive graphs of order with and prime. This generalises a recent result of Conder, Li … " - High-girth arc-transitive graphs

High-girth arc-transitive graphs

On distance, geodesic and arc transitivity of graphs

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. WebIn 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

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Web28 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 … 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 …

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.If m is the girth of Γ then the graph is called polygonal. We provide a construction of an infinite family of polygonal graphs of arbitrary odd girth with 2-arc transitive automorphism … WebGraphs are often a natural model in real world applications such as telecommunications networks, road and transport planning, economics and social …

Web25 de ago. de 2003 · ANALYSING FINITE LOCALLYs-ARC TRANSITIVE GRAPHS. MICHAEL GIUDICI, CAI HENG LI, AND CHERYL E. PRAEGER Abstract. We present a … 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.

WebDownloadable (with restrictions)! Let Γ be a finite simple undirected graph and G ≤ Aut(Γ). If G is transitive on the set of s-arcs but not on the set of (s+1)-arcs of Γ, then Γ is called (G, s)-transitive. For a connected (G, s)-transitive graph Γ of prime valency, the vertex-stabilizer Gα with α ∈ V(Γ) has been determined when Gα is solvable.

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 … req stuck_fs7200 remote approver.xlsxWeb1 de ago. de 2010 · We provide a construction of an infinite family of polygonal graphs of arbitrary odd girth with 2-arc transitive automorphism groups. References [1] … reqs technologiesWeb1 de ago. de 2010 · A near-polygonal graph is a graph @C which has a set C of m-cycles for some positive integer m such that each 2-path of @C is contained in exactly one cycle in C. If m is the girth of @C then the graph is called polygonal. reqs for death stepWebA. 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 … reqruting student for scholershipWeb28 de out. de 2009 · This paper gives a characterization of connected cubic s-transitive Cayley graphs.It is shown that, for s ≥ 3, every connected cubic s-transitive Cayley graph is a normal cover of one of 13 graphs: three 3-transitive graphs, four 4-transitive graphs and six 5-transitive graphs.Moreover, the argument in this paper also gives another … propolis moisture firming eye creamWeb1 de mar. de 2024 · It is proved that every such graph, with the exception of the Desargues graph on 20 vertices, is either a skeleton of a hexagonal tiling of the torus, the skeleton … propolis mouth sprayWeb9 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 ... propolis mouthwash recipe