Related papers: Automorphisms of Cayley graphs generated by transp…

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…

Let G be a right-angled Artin group. We use geometric methods to compute a presentation of the subgroup H of Aut(G) consisting of the automorphisms that send each generator to a conjugate of itself. This generalizes a result of McCool on…

We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…

The subdirect product of two finite groups $A$ and $B$ is defined as a subgroup of the direct product $A \times B$, which is a well-known notion in finite group theory. While it is clear that, under appropriate choices of sets of generators…

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers in which this locally bijective homomorphism is prescribed by an action of a subgroup of ${\rm Aut}(G)$. Regular…

We show that almost all circulant graphs have automorphism groups as small as possible. Of the circulant graphs that do not have automorphism group as small as possible, we give some families of integers such that it is not true that almost…

Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general…

A spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a…

In the paper Graphical complexity of products of permutation groups, M. Grech, A. Jez, A. Kisielewicz have proved that the direct product of automorphism groups of edge-colored graphs is itself the automorphism groups of an edge-colored…

Let $K$ be a field of characteristic $0$ and let $G$ and $H$ be connected commutative algebraic groups over $K$. Let $\text{Mor}_0(G,H)$ denote the set of morphisms of algebraic varieties $G \to H$ that map the neutral element to the…

A non-complete graph is \emph{$2$-distance-transitive} if, for $i=1,2$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance $i$ in the graph, there exists an element of the graph automorphism group that maps…

The power graph of a group $G$ is a graph with vertex set $G$, in which two vertices are adjacent if one is some power of the other. In the commuting graph, with $G$ as the vertex set, two vertices are joined by an edge if they commute in…

In this article we continue the study of automorphism groups of constant length substitution shifts and also their topological factors. We show that up to conjugacy, all roots of the identity map are letter exchanging maps, and all other…

In this paper, we give a characterization for a class of edge-transitive Cayley graphs, and provide methods for constructing Cayley graphs with certain symmetry properties. Also this study leads to construct and characterise a new family of…

Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on…

An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when the group of conjugating automorphisms of a graph product…

Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse…

For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…

Given a finite graph G there is a corresponding group given by the presentation with generators the vertices of G and a relation [x,y]=1 for generators x and y precisely when (x,y) is an edge of G. Such groups are known as partially…

Let $G$ be a connected graph on $n$ vertices and $1 \le k \le n-1$ an integer. The $k$-token graph of $G$ is the graph $F_k(G)$ whose vertices are all the $k$-subsets of vertices of $G$, two of which are adjacent whenever their symmetric…