Related papers: Coverings of Profinite Graphs
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
In this paper, we define the quotinet graphs. In particular, we introduce the boundary quotient graphs, admissible boundary quotient graphs and subgraph boundary qoutient graphs. By the property of the quotient spaces, the boundary…
In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this…
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
A profinite group equipped with an expansive endomorphism is equivalent to a one-sided group shift. We show that these groups have a very restricted structure. More precisely, we show that any such group can be decomposed into a finite…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…
Graph $G$ is $F$-saturated if $G$ contains no copy of graph $F$ but any edge added to $G$ produces at least one copy of $F$. One common variant of saturation is to remove the former restriction: $G$ is $F$-semi-saturated if any edge added…
Let $G$ be a group and let $K$ be a commensurated subgroup of $G$. Then there is a totally disconnected, locally compact (t.d.l.c.) group $\hat{G}_K$ that contains the profinite completion of $K$ as an open compact subgroup and also…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…
We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups.…
For a formation $\mathfrak{F}$ of finite groups, tight connections are established between the pro-$\mathfrak{F}$-topology of a finitely generated free group $F$ and the geometry of the Cayley graph $\Gamma(\hat{F_{\mathfrak{F}}})$ of the…
We define the cover number of a graph $G$ by a graph class $\mathcal P$ as the minimum number of graphs of class $\mathcal P$ required to cover the edge set of $G$. Taking inspiration from a paper by Harary, Hsu and Miller, we find an exact…
We study the subgroup structure of the \'etale fundamental group $\Pi$ of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond theorem for $\Pi$. As a consequence we show that most…
A conjecture of Berge suggests that every bridgeless cubic graph can have its edges covered with at most five perfect matchings. Since three perfect matchings suffice only when the graph in question is $3$-edge-colourable, the rest of cubic…
We prove that every connected locally finite regular graph has a double cover which is isomorphic to a Schreier graph.
We generalize the notion of an inverse sequence of graph covers from the zero-dimensional dynamical systems to any dynamical system.
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
Suppose that $F$ is a finite field and $R=M_n(F)$ is the ring of $n$-square matrices over $F$. Here we characterize when the Cayley graph of the additive group of $R$ with respect to the set of invertible elements of $R$, called the unitary…