Add to ORKGWe call a graph $k$-geodetic, for some $k\geq 1$, if it is connected and between any two vertices there are at most $k$ geodesics. It is shown that any hyperbolic group with a $k$-geodetic Cayley graph is virtually-free. Furthermore, in such a group the centraliser of any infinite order element is an infinite cyclic group. These results were known previously only in the case that $k=1$. A key tool used to develop the theorem is a new graph theoretic result concerning ``ladder-like structures'' in a $k$-geodetic graph.Comment: 12 pages, 11 figure
AbstractIn this paper we investigate some structural characterizations of geodetic graphs and prove ...
AbstractWe show a connection between 2-connected geodetic graphs of diameter two and certain geometr...
AbstractFor every pair of vertices u,v in a graph, a u-v geodesic is a shortest path from u to v. Fo...
AbstractGeneralizing Cook and Pryce's construction procedures for geodetic blocks, an operation in g...
AbstractA graph G is called strongly geodetic if two arbitrary vertices are connected by at most one...
summary:For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u, v]$ consists of $u$, ...
Abstract. Let (W;S) be a Coxeter system such that no two generators in S commute. Assume that the Ca...
AbstractA set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path be...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
AbstractA set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path be...
AbstractOre defined a graph to be geodetic if and only if there is a unique shortest path between tw...
summary:For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u, v]$ consists of $u$, ...
AbstractIn this paper we investigate some structural characterizations of geodetic graphs and prove ...
AbstractWe show a connection between 2-connected geodetic graphs of diameter two and certain geometr...
AbstractFor every pair of vertices u,v in a graph, a u-v geodesic is a shortest path from u to v. Fo...
AbstractGeneralizing Cook and Pryce's construction procedures for geodetic blocks, an operation in g...
AbstractA graph G is called strongly geodetic if two arbitrary vertices are connected by at most one...
summary:For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u, v]$ consists of $u$, ...
Abstract. Let (W;S) be a Coxeter system such that no two generators in S commute. Assume that the Ca...
AbstractA set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path be...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between tw...
AbstractA set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path be...
AbstractOre defined a graph to be geodetic if and only if there is a unique shortest path between tw...
summary:For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u, v]$ consists of $u$, ...
AbstractIn this paper we investigate some structural characterizations of geodetic graphs and prove ...
AbstractWe show a connection between 2-connected geodetic graphs of diameter two and certain geometr...
AbstractFor every pair of vertices u,v in a graph, a u-v geodesic is a shortest path from u to v. Fo...