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Displaying 301 – 320 of 430

Remark about a construction of some tournaments points of certain projective planes

Věroslav Jurák (1973)

Acta Universitatis Carolinae. Mathematica et Physica

Representation of undirected graphs by anticommutative conservative groupoids

Bohdan Zelinka (1994)

Mathematica Bohemica

The paper studies tolerances and congruences on anticommutative conservative groupoids. These groupoids can be assigned in a one-to-one way to undirected graphs.

Réseaux de Coxeter-Davis et commensurateurs

Frédéric Haglund (1998)

Annales de l'institut Fourier

For each integer $k \geq 6$ and each finite graph $L$ , we construct a Coxeter group $W$ and a non positively curved polygonal complex $A$ on which $W$ acts properly cocompactly, such that each polygon of $A$ has $k$ edges, and the link of each vertex of $A$ is isomorphic to $L$ . If $L$ is a “generalized $m$ -gon”, then $A$ is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on $Aut (L)$ for $Aut (A)$ to be non enumerable (which is satisfied if $L$ is a thick classical generalized $m$ -gon). On the other hand,...

Resolving sets of directed Cayley graphs for the direct product of cyclic groups

Demelash Ashagrie Mengesha, Tomáš Vetrík (2019)

Czechoslovak Mathematical Journal

A directed Cayley graph $C (Γ, X)$ is specified by a group $Γ$ and an identity-free generating set $X$ for this group. Vertices of $C (Γ, X)$ are elements of $Γ$ and there is a directed edge from the vertex $u$ to the vertex $v$ in $C (Γ, X)$ if and only if there is a generator $x \in X$ such that $u x = v$ . We study graphs $C (Γ, X)$ for the direct product $Z_{m} \times Z_{n}$ of two cyclic groups $Z_{m}$ and $Z_{n}$ , and the generating set $X = {(0, 1), (1, 0), (2, 0), \dots, (p, 0)}$ . We present resolving sets which yield upper bounds on the metric dimension of these graphs for $p = 2$ and $3$ .

Resonant delocalization for random Schrödinger operators on tree graphs

Michael Aizenman, Simone Warzel (2013)

Journal of the European Mathematical Society

We analyse the spectral phase diagram of Schrödinger operators $T + λ V$ on regular tree graphs, with $T$ the graph adjacency operator and $V$ a random potential given by $i i d$ random variables. The main result is a criterion for the emergence of absolutely continuous $(a c)$ spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials $a c$ spectrum appears at arbitrarily weak disorder $(λ ≪ 1)$ in an energy regime which extends beyond the spectrum of $\sim T$ . Incorporating...

Restricted walks in regular trees.

Ciobanu, Laura, Radomirović, Saša (2006)

The Electronic Journal of Combinatorics [electronic only]

Rigidity of graph products of groups.

Radcliffe, David G. (2003)

Algebraic & Geometric Topology

Ring elements as sums of units

Charles Lanski, Attila Maróti (2009)

Open Mathematics

In an Artinian ring R every element of R can be expressed as the sum of two units if and only if R/J(R) does not contain a summand isomorphic to the field with two elements. This result is used to describe those finite rings R for which Γ(R) contains a Hamiltonian cycle where Γ(R) is the (simple) graph defined on the elements of R with an edge between vertices r and s if and only if r - s is invertible. It is also shown that for an Artinian ring R the number of connected components of the graph...

Roughness in $G$ -graphs

Bibi N. Onagh (2020)

Commentationes Mathematicae Universitatis Carolinae

$G$ -graphs are a type of graphs associated to groups, which were proposed by A. Bretto and A. Faisant (2005). In this paper, we first give some theorems regarding $G$ -graphs. Then we introduce the notion of rough $G$ -graphs and investigate some important properties of these graphs.

Sachs triangulations, generated by dessins d'enfant, and regular maps

Heinz-Jürgen Voss (1997)

Mathematica Slovaca

Self-dual regular maps from medial graphs.

Archdeacon, D., Širáň, J., Škoviera, M. (1992)

Acta Mathematica Universitatis Comenianae. New Series

Self-invariant 1-factorizations of complete graphs and finite Bol loops of exponent 2.

Baumeister, Barbara, Stein, Alexander (2010)

Beiträge zur Algebra und Geometrie

Semidefinite functions on categories.

Lovász, László, Schrijver, Alexander (2009)

The Electronic Journal of Combinatorics [electronic only]

Semisymmetric cubic graphs of order $4 p^{n}$ .

Alaeiyan, Mehdi, Onagh, B.N. (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

Sense Preserving Groups of Polyhedral Graphs.

L. Babai, W. Imrich (1975)

Monatshefte für Mathematik

Sharply transitive 1-factorizations of complete multipartite graphs.

Mazzuoccolo, Giuseppe, Rinaldi, Gloria (2010)

The Electronic Journal of Combinatorics [electronic only]

Simplicial approximation and low-rank trees.

P.B. Shalen, H. Gillet, R.K. Skora (1991)

Commentarii mathematici Helvetici

Simultaneous representations in discrete structures

Věra Trnková (1986)

Commentationes Mathematicae Universitatis Carolinae

Sofic groups are not locally embeddable into finite Moufang loops

Heghine Ghumashyan, Jaroslav Guričan (2022)

Mathematica Bohemica

We shall show that there exist sofic groups which are not locally embeddable into finite Moufang loops. These groups serve as counterexamples to a problem and two conjectures formulated in the paper by M. Vodička, P. Zlatoš (2019).

Some additive applications of the isoperimetric approach

Yahya O. Hamidoune (2008)

Annales de l’institut Fourier

Let $G$ be a group and let $X$ be a finite subset. The isoperimetric method investigates the objective function $| (X B) ∖ X |$ , defined on the subsets $X$ with $| X | \geq k$ and $| G ∖ (X B) | \geq k$ , where $X B$ is the product of $X$ by $B$ .In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure...

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