Related papers: Lifting Voltages in Graph Covers
A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of…
We prove that the notion of a derived voltage graph comes from an adjunction between the category of voltage graphs and a category of group labeled graphs.
In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship between lifted digraphs of voltage digraphs and line…
The derived graph of a voltage graph consisting of a single vertex and two loops of different voltages is a circulant graph with two generators. We characterize the automorphism groups of connected, two-generator circulant graphs, and give…
This article proposes an effective criterion for lifting automorphisms along regular coverings of graphs, with the covering transformation group being any finite abelian group.
We consider lifting eigenvalues and eigenvectors of graphs to their {\em factored lifts}, derived by means of a {\em combined voltage assignment} in a group. The latter extends the concept of (ordinary) voltage assignments known from…
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…
A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given…
This paper proves results about the Jacobians of a certain family of covering graphs, $Y$, of a base graph $X$, that is constructed from an assignment of elements from a group $G$ to the edges of $X$ ($G$ is called the voltage group and $Y$…
Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above…
Given a finite connected simple graph $\Gamma$, and a subgroup $G$ of its automorphism group, a general method for finding all finite abelian regular coverings of $\Gamma$ that admit a lift of each element of $G$ is developed. As an…
It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…
An ordinary voltage graph embedding of a graph in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph $G$ in a surface with voltage group $A$ and a…
Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. Assuming rational independence of edge lengths, necessary and sufficient…
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group $G$. A classical construction of Gross and Tucker associates to every voltage graph with vertex set $V$ a so-called derived graph with vertex…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
This paper describes a general method for representing $k$-token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and Johnson graphs as lift graphs on cyclic groups. As an…
We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift $\Gamma^{\alpha}$ of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its…
We study a family of positive weighted well-covered graphs, which we call levelable graphs, that are related to a construction of level artinian rings in commutative algebra. A graph $G$ is levelable if there exists a weight function with…
Classical geometric and topological operations on polyhedra, maps and polytopes often give rise to structures with the same symmetry group as the original one, but with more flags. In this paper we introduce the notion of voltage operations…