Related papers: Arithmetic graphs of finite groups

We study semifinite harmonic functions on arbitrary branching graphs. We give a detailed exposition of an algebraic method which allows one to classify semifinite indecomposable harmonic functions on some multiplicative branching graphs.…

We consider the oriented graph whose vertices are isomorphism classes of finitely generated groups, with an edge from G to H if, for some generating set T in H and some sequence of generating sets S_i in G, the marked balls of radius i in…

In this note, we define a new graph $\Gamma_d(G)$ on a finite group $G$, where $d$ is a divisor of $|G|$. The vertices of $\Gamma_d(G)$ are the subgroups of $G$ of order $d$ and two subgroups $H_1$ and $H_2$ of $G$ are said to be adjacent…

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…

An automorphism group of a graph $G$ is the set of all permutations of the vertex set of $G$ that preserve adjacency and non adjacency of vertices in a graph. A fixing set of a graph $G$ is a subset of vertices of $G$ such that only the…

Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…

The prime graph question asks whether the Gruenberg-Kegel graph of an integral group ring $\mathbb Z G$ , i.e. the prime graph of the normalised unit group of $\mathbb Z G$ coincides with that one of the group $G$. In this note we prove for…

We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy…

We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive…

Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-arithmetic group to (the isomorphism class of) its…

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph…

In this paper, we define several measures induced by a finite directed graph. The study themselves is interesting ont only in the noncommutative probability point of view but also in the algebraic structure point of view, since to define…

The undirected power graph (or simply power graph) of a group $G$, denoted by $P(G)$, is a graph whose vertices are the elements of the group $G$, in which two vertices $u$ and $v$ are connected by an edge between if and only if either…

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…

A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…

We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…

In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.

Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same…