Related papers: Transitive graphs uniquely determined by their loc…
For each of the 14 classes of edge-transitive maps described by Graver and Watkins, necessary and sufficient conditions are given for a group to be the automorphism group of a map, or of an orientable map without boundary, in that class.…
This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.
We define train track maps for graphs-of-groups $\cal G$ and exhibit the precise conditions under which the fundamental finiteness properties known for classical train track maps extend to this generalization. These finiteness properties…
Extending the work of Godsil and others, we investigate the notion of the inverse of a graph (specifically, of bipartite graphs with a unique perfect matching). We provide a concise necessary and sufficient condition for the invertibility…
An $H$-decomposition of a graph $\Gamma$ is a partition of its edge set into subgraphs isomorphic to $H$. A transitive decomposition is a special kind of $H$-decomposition that is highly symmetrical in the sense that the subgraphs (copies…
An inaccessible, vertex transitive, locally finite graph is described. This graph is not quasi-isometric to a Cayley graph.
The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…
In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a…
A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let $\Gamma$ be a connected graph…
Distance-hereditary graphs are known to be the graphs that are totally decomposable for the split decomposition. We characterise distance-hereditary graphs whose complement is also distance-hereditary by their split decomposition and by…
We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of…
Consider the graph obtained by superposition of an independent pair of uniform infinite non-crossing perfect matchings of the set of integers. We prove that this graph contains at most one infinite path. Several motivations are discussed.
If $v$ is an eigenvector for eigenvalue $\lambda$ of a graph $X$ and $\alpha$ is an automorphism of $X$, then $\alpha(v)$ is also an eigenvector for $\lambda$. Thus it is rather exceptional for an eigenvalue of a vertex-transitive graph to…
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random…
In this paper authors consider representations of graphs in Hilbert spaces applying a restriction of local scalarity on them. It enables to obtain a theory, similar to the classical theory of representations of graphs in vector spaces. In…
We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the…
We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph…
In this paper we show a correspondence between directed graphs and bipartite undirected graphs with a perfect matching, that allows to study properties of directed graphs through the properties of the corresponding undirected graphs. In…
Distance-regular graphs have many beautiful combinatorial properties. Distance-transitive graphs have very strong symmetries, and they are distance-regular, i.e. distance-transitivity implies distance-regularity. In this paper, we give…
The modular decomposition of a graph is a canonical representation of its modules. Algorithms for computing the modular decomposition of directed and undirected graphs differ significantly, with the undirected case being simpler, and…