A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Distance Sequences In Locally Infinite Vertex-Transitive Digraphs

2006
*
Combinatorica
*

We prove that the out-

doi:10.1007/s00493-006-0033-y
fatcat:xckh6n2ezzbqjlv67ctmplzism
*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 ... vertex-*transitive**graphs*, and has asked if "valleys" can occur*in*the locally*infinite*case [B] . ...##
###
Distance Sequences of Locally Infinite Primitive Graphs
[article]

2020
*
arXiv
*
pre-print

*In*this paper, we prove a classification of the possible

*distance*sequences of locally

*infinite*primitive

*graphs*. ... We also prove a constraint on the

*distance*sequences of locally finite

*infinite*

*graphs*. ... Pegden

*in*[2] has noted that for locally

*infinite*vertex-

*transitive*

*graphs*, the possible

*distance*sequences are limited. ...

##
###
FINITE VORONOI DECOMPOSITIONS OF INFINITE VERTEX TRANSITIVE GRAPHS

2013
*
Journal of Topology and Analysis (JTA)
*

*In*this paper, we consider the Voronoi decompositions of an arbitrary

*infinite*vertex-

*transitive*

*graph*G. ... We show that all vertex

*transitive*

*graphs*with polynomial growth have a finite s(G); vertex

*transitive*

*graphs*with

*infinitely*many ends have an

*infinite*s(G); the lamplighter

*graph*LL(Z), which has exponential ... Every

*infinite*vertex-

*transitive*

*graph*G has s(G) ≥ 2. Proof. Let v be a vertex

*in*G. ...

##
###
A census of infinite distance-transitive graphs

1998
*
Discrete Mathematics
*

This paper describes some classes of

doi:10.1016/s0012-365x(98)00063-6
fatcat:tac5nwiyrnh4xboixwqzyk2hga
*infinite**distance*-*transitive**graphs*. It has no pretensions to give a complete list, but concentrates on*graphs*which have no finite analogues. ... A very complete reference on finite*distance*-*transitive**graphs*is the book of Brouwer et al. [l]. By contrast, the theory of*infinite**distance*-*transitive**graphs*is open. ... However, only*in*two cases do we get*distance*-*transitive**graphs*: ...##
###
Infinite vertex-transitive, edge-transitive non-$1$-transitive graphs

1989
*
Proceedings of the American Mathematical Society
*

We show that every vertex-

doi:10.1090/s0002-9939-1989-0973847-6
fatcat:ycdyzvniwjasfata7p4livwny4
*transitive*, edge-*transitive**graph*of odd valence and subexponential growth is 1-*transitive*, thus extending to*infinite**graphs*a theorem of W. T. Tutte for finite*graphs*. ... We describe a number of counterexamples*in*the case of exponential growth. ... Acknowledgment The authors are grateful to the Laboratoire de Recherche en Informatique, Université de Paris-Sud, Orsay, France, for having brought us there at the same time*in*February 1986. ...##
###
Sum rules for effective resistances in infinite graphs

2017
*
Journal of Statistical Mechanics: Theory and Experiment
*

Extending work of Foster, Doyle, and others, we show how the Foster Theorems, a family of results concerning effective resistances on finite

doi:10.1088/1742-5468/aa6503
fatcat:f6br43njcffj3jsfc7ueyy44j4
*graphs*, can*in*certain cases be extended to*infinite**graphs*. ... The results are illustrated with some of the most common grids*in*the plane, including the square, triangular, and hexagonal grids. ... As was noted*in*Section 3, Foster's First and Second easily give the resistances between adjacent points*in*1-arc*transitive**graphs*and points of*distance*2*in*2-arc*transitive**graphs*, with the corresponding ...##
###
Page 654 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

*In*particular, they have

*infinitely*many ends. The author shows that for an

*infinite*, locally finite, connected

*graph*with more than one end, 2-

*distance*

*transitivity*implies

*distance*

*transitivity*. ... (ICE-UICE-SI; Reykjavik)

*Distance*-

*transitivity*

*in*

*infinite*

*graphs*. (English summary) J. Combin. Theory Ser. B 60 (1994), no. 1, 36-39. ...

##
###
A note on the growth of transitive graphs

1988
*
Discrete Mathematics
*

Let X be a locally finite, connected, growth if and only if X is a strip.

doi:10.1016/0012-365x(88)90138-0
fatcat:elz23bssbzbyhcxearetifkhhy
*infinite*,*transitive**graph*. We show that X has linear 0012~365X/88/$3.50 @ 1988, Elsevier !&Science Publishers B.V. (North- ...*In*Proposition 2.1 we prove that a*graph*X cannot have linear growth if n(E) is*infinite*for some E E E(X). 'Ihen we show that there exist no*transitive**graphs*X of linear growth with only one end. ... By T,(A), m 2 0, we denote the set of all vertices y E V(X) of*distance*m from x. Further H,(X) = UO F(X). Let v be a fixed vertex*in*a connected*graph*X. ...##
###
Page 3540 of Mathematical Reviews Vol. , Issue 93g
[page]

1993
*
Mathematical Reviews
*

A

*graph*T is said to be affine*distance**transitive*if some group G of automorphisms acting*distance**transitively*on IT has a regular normal elementary abelian subgroup N. ... This paper gives a classification of a certain family of affine*distance**transitive**graphs*. ...##
###
Percolation on Transitive Graphs as a Coalescent Process: Relentless Merging Followed by Simultaneous Uniqueness
[chapter]

1999
*
Perplexing Problems in Probability
*

Percolation on

doi:10.1007/978-1-4612-2168-5_4
fatcat:vzh6zo4j65e6vcuytml3oq3vci
*transitive**graphs*...*In*fact, this holds*in*the larger class of semi-*transitive**graphs*. ... Theorem 1.3 Let G be an*infinite*, locally finite, connected, quasi-*transitive**graph*, and let p c and p u be as*in*Theorem 1.2. ...##
###
Page 2460 of Mathematical Reviews Vol. , Issue 2000d
[page]

2000
*
Mathematical Reviews
*

The

*graph*I is said to be*distance*-*transitive*if it admits a*distance*-*transitive*group. This paper outlines a program for classifying the finite*distance*-*transitive**graphs*. ... A subgroup G of automorphisms of a*graph*T is said to be COMBINATORICS 2460*distance*-*transitive*on I if, for all i between 0 and the diameter of I, G is*transitive*on the set of ordered pairs of vertices ...##
###
Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
[article]

2016
*
arXiv
*
pre-print

We prove that critical percolation on any quasi-

arXiv:1605.05301v1
fatcat:7vvwfzbvdvebxflczm2y7f2zgi
*transitive**graph*of exponential volume growth does not have a unique*infinite*cluster. ... This allows us to deduce from earlier results that critical percolation on any*graph**in*this class does not have any*infinite*clusters. ... Given a*graph*G, we write B(x, r) to denote the*graph**distance*ball of radius r about a vertex x of G. ...##
###
Fairness, distances and degrees

1992
*
Theoretical Computer Science
*

We show the identity between sets of fair computations

doi:10.1016/0304-3975(92)90390-2
fatcat:gg2jnqhxy5b2zirqi3tauag2ty
*in*recursive*transition**graphs*, sets of cluster points of finite computations for II: ultra-metrics refining the Baire metrics, and II! ... Yoccoz, Fairness,*distances*and degrees, Theoretical Computer Science 97 (1992) 131-142. ...*Infinite*paths*in*a recursive tree may be seen as*infinite*computations*in*a recursive*transition**graph*with a recursive set of sink states. ...##
###
Exponential decay of connectivity and uniqueness in percolation on finite and infinite graphs
[article]

2016
*
arXiv
*
pre-print

We give an upper bound for the uniqueness

arXiv:1610.04897v1
fatcat:tnfdvilumbdvhdhazbbek3y5ca
*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. ... We give lower bounds for all three*transitions*usually associated with site percolation on*infinite**graphs*. We also identify a region of p where connectivity decays exponentially with the*distance*. ...##
###
On distance-balanced graphs

2010
*
European journal of combinatorics (Print)
*

It is shown that the

doi:10.1016/j.ejc.2009.10.006
fatcat:nxlayk3w4veobo7tnkjmtjvwji
*graphs*for which the Szeged index equals G ·|G | 2 4 are precisely connected, bipartite,*distance*-balanced*graphs*. This enables us to disprove a conjecture proposed*in*[M.H. ...*Infinite*families of*distance*-balanced, non-regular*graphs*that are prime with respect to the Cartesian product are also constructed. ... [10] constructed an*infinite*family of semisymmetric*graphs*which are not*distance*-balanced. (A regular*graph*is called semisymmetric if it is edge-*transitive*but not vertex-*transitive*[11] .) ...
« Previous

*Showing results 1 — 15 out of 91,601 results*