Related papers: Paley and the Paley graphs
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of…
The group of causal automorphisms on Minkowski space-time is given and its structure is analyzed.
We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.
In this paper, we study the metric dimension of Cayley graphs. Specially, we present a complete characterization of Cayley graphs on Abelian groups whose metric dimension is two.
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
Given a finite field, one can form a directed graph using the field elements as vertices and connecting two vertices if their difference lies in a fixed subgroup of the multiplicative group. If -1 is contained in this fixed subgroup, then…
We investigate subsets of the symmetric group with structure similar to that of a graph. The trees of these subsets correspond to minimal conjugate generating sets of the symmetric group. There are two main theorems in this paper. The first…
We record for reference a detailed description of the automorphism groups of the groups of order $p^{2} q$, where $p$ and $q$ are distinct primes.
The description of the automorphism group of group $<a, b; [a^m,b^n]=1>$ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.
Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.
Barbieri recently showed that the finite graphs realising any given finite automorphism group have unbounded genus, answering a question of Cornwell et al. In this note we give a short proof of a stronger result: they have unbounded clique…
For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…
The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel…
Various spaces of symmetries of a structure are naturally endowed with both an algebraic and a topological structure. For example, the automorphism group of a structure is, on top of being a group, a topological group when equipped with the…
We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.
We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.
We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related to each other through regular coverings and parallel…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.