High-girth arc-transitive graphs

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

TETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED …

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 … 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 … photo handball france https://selbornewoodcraft.com

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

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 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. 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. photo handball a imprimer

On distance, geodesic and arc transitivity of graphs

Category:Cubic s-arc transitive Cayley graphs - ScienceDirect

Tags:High-girth arc-transitive graphs

High-girth arc-transitive graphs

Cubic s-arc transitive Cayley graphs - ScienceDirect

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 … 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 …

High-girth arc-transitive graphs

Did you know?

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. … 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

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 … WebThis 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 …

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 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 …

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 ...

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 how does going to space affect your bodyWeb28 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 … photo handling programsWebWe 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 … how does gojo flyWebAn 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. how does gojo\u0027s infinity workWeba 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]. photo handicap et sportWeb3 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... photo handling glovesWebGraphs are often a natural model in real world applications such as telecommunications networks, road and transport planning, economics and social … how does going to rome change someone