High-girth arc-transitive graphs

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August undefined, 2024

WebWe 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 … 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. …

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

WebTETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED VERTEX-STABILIZERS PRIMOŽ POTOCNIK, PABLO SPIGAˇ and GABRIEL VERRET (Received … 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 … cowculus t shirt

Cubic s-arc transitive Cayley graphs - ScienceDirect

Web28 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 … Web1 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] … 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), … disney amc showtimes

An inﬁnite family of biquasiprimitive 2-arc transitive cubic graphs

Small vertex‐transitive and Cayley graphs of girth six and given ...

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 … disney america holidaysWebconstructed 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- cow culling rate

"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 … " - High-girth arc-transitive graphs

High-girth arc-transitive graphs

Finite s -Arc Transitive Graphs of Prime-Power Order - OUP …

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 ... Web1 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 …

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Webtransitive graphs that are s-arc transitive but not (s+1)-arc transitive. More-over, there exist geodesic transitive graphs that are s-arc transitive but not (s+1)-arc transitive with arbitrarily large diameter if and only if s ∈ {1,2,3}. Theorem 1.1 is proved in Section 3 by analysing some well-known families ofdistance transitive graphs ... WebGraphs are often a natural model in real world applications such as telecommunications networks, road and transport planning, economics and social …

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. 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 …

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 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 …

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 ...

Webarc-transitive graphs with vertex stabilizer D8 and order 10752, with 10752 being the smallest order of connected tetravalent half-arc-transitive graphs with vertex stabilizer … disney amc theaterWebArc-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 … disney americana magic bandWeb9 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 ... cow cullingWeb1 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 … cow cuddling new hampshireWebAn 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 … cow culling definitionWebthe corresponding Tanner graphs have girth greater than four. We analyse properties of the obtained codes and present bounds for the code parameters, ... Keywords: LDPC code, cubic graph, arc-transitive graph, bipartite graph MSC 2024 Codes: 94B05, 05C99 1 arXiv:2002.06690v1 [math.CO] 16 Feb 2024. 1 Introduction and preliminaries cow cupcake linersWeb16 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 disney american dragon jake long both intros