25,377 Hits in 3.7 sec

A characterization of locally finite vertex-transitive graphs

Carsten Thomassen
1987 Journal of combinatorial theory. Series B (Print)  
A locally finite graph G with no isolated vertices is vertex-transitive if and only if all its vertex-deleted subgraphs G -v are isomorphic. '  ...  Let G be a locally finite graph without isolated vertices. Then G is vertex-transitive if and only if all its vertex-deleted subgraphs are isomorphic.  ...  INTRODUCTION If a graph G is vertex-transitive, then clearly all of its vertex-deleted subgraphs G-U are isomorphic.  ... 
doi:10.1016/0095-8956(87)90033-5 fatcat:dgd3v32rjnavxgbpwie242gynm

Imprimitivity of locally finite, 1-ended, planar graphs

Jozef Širáň, Mark E. Watkins
2012 Ars Mathematica Contemporanea  
Using results from group theory, we offer a concise proof of the imprimitivity of locally finite, vertex-transitive, 1-ended planar graphs, a result previously established by J .E. Graver and M. E.  ...  Watkins (2004) using graph-theoretical methods.  ...  The idea for this note came about in late 2004 while the first author was affiliated with the University of Auckland and the second author was visiting at the invitation of C. Paul Bonnington.  ... 
doi:10.26493/1855-3974.213.fcd fatcat:fs644jkejnaotnrf72oetli3vm

A note on bounded automorphisms of infinite graphs

Chris D. Godsil, Wilfried Imrich, Norbert Seifter, Mark E. Watkins, Wolfgang Woess
1989 Graphs and Combinatorics  
Let X be a connected locally finite graph with vertex-transitive automorphism group.  ...  If X has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup of AUT(X) and the action of AUT(X) on V(X) is imprimitive if X is not  ...  However, Trofimov's characterization of vertex-transitive connected locally finite graphs with polynomial growth [12] shows that the automorphism groups of these graphs are still very close to nilpotent  ... 
doi:10.1007/bf01788688 fatcat:3fojkrh5szftjleyukajllpyt4

Distance Sequences In Locally Infinite Vertex-Transitive Digraphs

Wesley Pegden
2006 Combinatorica  
We prove that the out-distance sequence {f + (k)} of a vertex-transitive digraph of finite or infinite degree satisfies f + (k + 1) ≤ f + (k) 2 for k ≥ 1, where f + (k) denotes the number of vertices at  ...  As a corollary, we prove that for a connected vertextransitive undirected graph of infinite degree d, we have f (k) = d for all k, 1 ≤ k < diam(G). This answers a question  ...  Babai has pointed out that results on local expansion of vertex-transitive graphs [BS] limit the possible pathologies (i.e., hills and valleys) in the distance sequences of locally finite undirected  ... 
doi:10.1007/s00493-006-0033-y fatcat:xckh6n2ezzbqjlv67ctmplzism

Topological groups and infinite graphs

Wolfgang Woess
1991 Discrete Mathematics  
We show how results concerning infinite, locally finite, vertex-symmetric graphs can be related with the structure theory of topological groups, when the latter is applied to automorphism groups of the  ...  graphs.  ...  to an arbitrary locally finite, vertex-symmetric graph r with polynomial growth.  ... 
doi:10.1016/0012-365x(91)90348-6 fatcat:3u5vn6opynacnnrbq2ktsxwjr4

Some conditions for 1-transitivity

Mark E. Watkins
1992 Discrete Mathematics  
., Some conditions for l-transitivity, Discrete Mathematics 109 (1992) 289-296. Every l-transitive finite or infinite graph is clearly both vertex-transitive and edge-transitive.  ...  Finally, a new infinite family of infinite graphs is constructed that are vertex-transitive and edge-transitive but not l-transitive. 0012-365X/92/$05.00 0 1992 -Elsevier Science Publishers B.V.  ...  Let r be infinite, locally finite, planar, vertex-trar?  ... 
doi:10.1016/0012-365x(92)90299-u fatcat:n3re7qoqkvhglee4d3y7d65eta

A note on the growth of transitive graphs

W. Imrich, N. Seifter
1988 Discrete Mathematics  
Let X be a locally finite, connected, growth if and only if X is a strip. infinite, transitive graph. We show that X has linear 0012~365X/88/$3.50 @ 1988, Elsevier !&Science Publishers B.V. (North-  ...  Hence the 8 span X. 0 Note a&d ti proofi We should like to point out that Trofimov [9] has recently characterized vertex-transitive locally finite connected graphs of polynomial growth.  ...  There is no connected, locally finite, transitive graph X of linear growth with only one end= Proof. Choose a vertex x E V(X).  ... 
doi:10.1016/0012-365x(88)90138-0 fatcat:elz23bssbzbyhcxearetifkhhy

Page 6927 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
In the first part of the paper a criterion for a group to be iso- morphic to the stabilizer of a vertex in a vertex-transitive group of automorphisms of a connected locally finite graph is given.  ...  The criterion is that a group is iso- morphic to the stabilizer of a vertex in a vertex-transitive group of automorphisms of a connected locally finite graph if and only if there exists a sparse commensurative  ... 

Page 769 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
An answer is provided if X is a locally finite graph such that a finitely generated, infinite, abelian group acts almost transitively on it.  ...  Suppose, moreover, that there is a vertex-transitive group G < Aut(X’) with finite vertex stabilizers.  ... 

Page 477 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
It contains discussions of (a) Tutte’s theorem that finite trivalent s-transitive graphs must have s<5, (b) [locally] s-transitive graphs with minimal girth and their connection with groups having (B,N  ...  This is a report on what is known at present about [locally] s-transitive graphs.  ... 

Exponential decay of connectivity and uniqueness in percolation on finite and infinite graphs [article]

Kathleen E. Hamilton, Leonid P. Pryadko
2016 arXiv   pre-print
We give an upper bound for the uniqueness transition on an arbitrary locally finite graph G in terms of the limit of the spectral radii ρ[ H( G_t)] of the non-backtracking (Hashimoto) matrices for an increasing  ...  With the added assumption of strong local connectivity for the oriented line graph (OLG) of G, connectivity on any finite subgraph G'⊂ G decays exponentially for p<(ρ[ H( G^')])^-1.  ...  Consider site percolation on a locally finite graph G characterized by the Hashimoto matrix H. Then p T ≥ 1/ gr 1 H, p c ≥ 1/ gr 1 H.  ... 
arXiv:1610.04897v1 fatcat:tnfdvilumbdvhdhazbbek3y5ca

Page 4151 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
Let X be a (finite or infinite) vertex-transitive graph and let S be a finite subset of the vertices. If X is finite, we also assume |S| < |V(X)|/2.  ...  The double covering B(X) of a finite graph X is a certain bipartite graph whose vertex set consists of two copies of the vertex set of X.  ... 

Lattices in graphs with polynomial growth

András Lukács, Norbert Seifter
1998 Discrete Mathematics  
We present results on the structure of graphs with polynomial growth. For certain classes of these graphs we prove that they contain subgraphs which are similar to the lattice graph L d .  ...  These results are then applied to investigate isoperimetric properties of certain classes of graphs with polynomial growth.  ...  In [Tr1] the following characterization of those graphs which admit a transitive group of bounded automorphisms was given: Theorem 2.1. Let X be a connected, locally finite graph.  ... 
doi:10.1016/s0012-365x(97)00194-5 fatcat:x2gwtbtgx5cbxldaiqvynjckjm

Page 924 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
This paper is a contribution to the classification of finite vertex- primitive distance-transitive graphs.  ...  A graph X is called semisymmetric if it is regular and edge- transitive but not vertex transitive.  ... 

The vertex-transitive TLF-planar graphs [article]

D. Renault
2004 arXiv   pre-print
We characterize these graphs with a finite local representation and a special kind of finite state automaton named labeling scheme.  ...  We consider the class of the topologically locally finite (in short TLF) planar vertex-transitive graphs, a class containing in particular all the one-ended planar Cayley graphs and the normal transitive  ...  A Enumerations of vertex-transitive graphs In the following sections, we enumerate all locally finite planar vertex-transitive graphs of small inner degree (from 3 to 4).  ... 
arXiv:cs/0412078v1 fatcat:gpavzsicobfvhgyzdcoy3r2nn4
« Previous Showing results 1 — 15 out of 25,377 results