High-girth arc-transitive graphs

Author: dlox

August undefined, 2024

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 … 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 …

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

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 p prime, then s = 2 or 3; further, either s = 3 and Γ is a normal … 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 how does ponyboy lie to himself in chapter 11

A construction of an infinite family of 2-arc transitive polygonal ...

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

The girth of cubic graphs Royal Holloway Repository

Two-arc Transitive Near-polygonal Graphs SpringerLink

Web15 de mar. de 2011 · However, beside a well-known family of exceptional graphs, related to the lexicographic product of a cycle with an edgeless graph on two vertices, only a few such infinite families of graphs are known. In this paper, we present two more families of tetravalent arc-transitive graphs with large vertex-stabilizers, each significant for its … 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 … photo of woman screamingWebThe Cayley graph F is denoted by Cay(G, S). Cayley graphs stem from a type of diagram now called a Cayley color diagram, introduced by Cayley in 1878. In this paper, we … how does pool chlorine work

"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. " - High-girth arc-transitive graphs

High-girth arc-transitive graphs

$arXiv:2002.06690v1 [math.CO] 16 Feb 2024$

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 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 …

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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 … 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 ...

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- Web16 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

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 … 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 …

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 …

Webthe 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 how does polyphemus trap the hellenesWeb9 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 ... how does polyphemus treat odysseusWeb1 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] … how does polymer work in water treatmentWebThis particular graph has 58 vertices - the 32 known trivalent graphs with 60 vertices are also catalogued and in some cases constructed. We prove the existence of vertex … how does polymer banknote workWeb1 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. how does ponyboy know cherry and marciaWeb1 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. … photo of wombatWebtransitive 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 ... photo of wood tick