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In this paper, by a travel groupoid is meant an ordered pair $(V, *)$ such that $V$ is a nonempty set and $*$ is a binary operation on $V$ satisfying the following two conditions for all $u, v \in V$ : $(u * v) * u = u; if (u * v) * v = u, then u = v .$ Let $(V, *)$ be a travel groupoid. It is easy to show that if $x, y \in V$ , then $x * y = y$ if and only if $y * x = x$ . We say that $(V, *)$ is on a (finite or infinite) graph $G$ if $V (G) = V$ and $E (G) = {{u, v} u, v \in V and u \neq u * v = v} .$ Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.

Travel groupoids on infinite graphs

Jung Rae Cho, Jeongmi Park, Yoshio Sano (2014)

Czechoslovak Mathematical Journal

The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set $V$ and a binary operation $*$ on $V$ satisfying two axioms. We can associate a graph with a travel groupoid. We say that a graph $G$ has a travel groupoid if the graph associated with the travel groupoid is equal to $G$ . Nebeský gave a characterization of finite graphs having a travel groupoid. In this paper, we study travel groupoids on infinite graphs....

Trees and monotone structures.

T. E. Hays (1976/1977)

Semigroup forum

Trees and reflection groups.

Talpo, Humberto Luiz, Firer, Marcelo (2005)

The Electronic Journal of Combinatorics [electronic only]

Trees, band monoids, and formal languages.

H. Sezinando, O. Neto (1996)

Semigroup forum

Trees in commtative nil-semigroups of index two

Václav Flaška, A. Jančařík, Vítězslav Kala, Tomáš Kepka (2007)

Acta Universitatis Carolinae. Mathematica et Physica

Trees of manifolds and boundaries of systolic groups

Paweł Zawiślak (2010)

Fundamenta Mathematicae

We prove that the Pontryagin sphere and the Pontryagin nonorientable surface occur as the Gromov boundary of a 7-systolic group acting geometrically on a 7-systolic normal pseudomanifold of dimension 3.

Trees of manifolds with boundary

Paweł Zawiślak (2015)

Colloquium Mathematicae

We introduce two new classes of compacta, called trees of manifolds with boundary and boundary trees of manifolds with boundary. We establish their basic properties.

Trees, valuations, and the Bieri-Neumann-Strebel invariant.

K.S. Brown (1987)

Inventiones mathematicae

Treillis de Cayley des groupes de Coxeter finis. Constructions par récurrence et décompositions sur des quotients

Claude Le Conte de Poly-Barbut (1997)

Mathématiques et Sciences Humaines

Cet article, offert à André Lentin lors du colloque du 23 février 1996 organisé en son honneur, a pour objet de montrer que le treillis étiqueté obtenu à partir de l’ordre faible sur un Coxeter fini $(W, S)$ , et le groupe lui-même, peuvent être construits à partir d’un sous-groupe parabolique quelconque $W_{J}$ , du quotient associé $W^{J}$ et d’une fonction de $W^{J} \times J$ dans $S \cup ⊘$ . Cette méthode permet en particulier la construction par récurrence des groupes et treillis des quatre familles infinies de Coxeter finis irréductibles...

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Translational hulls of polynomially related semigroups

Translations in Idempotent Groupoids

Translations of commutative unique factorization semigroups.

Transvectants des formes binaires et représentations des groupes binaires polyhedraux

Travaux de J. Stallings sur la décomposition des groupes en produits libres

Travaux de Quillen sur la cohomologie des groupes

Travel groupoids