Related papers: On monoid graphs

A monoid is said to be special if it admits a presentation in which all defining relations are of the form $w = 1$. Groups are familiar examples of special monoids. This article studies the geometric and structural properties of the Cayley…

We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$…

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.

Two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.

We study groupoids and semigroup C*-algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gives rise to a submonoid of the fundamental group which is…

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…

This paper establishes connections between the structure of a semigroup and the minimum spans of distance labellings of its Cayley graphs. We show that certain general restrictions on the minimum spans are equivalent to the semigroup being…

We study bipartite distance-regular Cayley graphs with diameter three or four. We give sufficient conditions under which a bipartite Cayley graph can be constructed on the semidirect product of a group -- the part of this bipartite Cayley…

Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there…

Graphs and various graph-like combinatorial structures, such as preorders and hypergraphs, are ubiquitous in programming. This paper focuses on representing graphs in a purely functional programming language like Haskell. There are several…

Ara\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest…

This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…

In this paper we investigate properties of the Artin monoid Cayley graph. This is the Cayley graph of an Artin group $A_\Gamma$ with respect to the (infinite) generating set given by the associated Artin monoid $A^+_\Gamma$. In a previous…

We introduce Cayley posets as posets arising naturally from pairs $S<T$ of semigroups, much in the same way that Cayley graph arises from a (semi)group and a subset. We show that Cayley posets are a common generalization of several known…

We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+o(n)$. This can be seen as a directed graph…

We introduce and study a strong "thin triangle"' condition for directed graphs, which generalises the usual notion of hyperbolicity for a metric space. We prove that finitely generated left cancellative monoids whose right Cayley graphs…

Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural…

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 show that doubling at some large scale in a Cayley graph implies uniform doubling at all subsequent scales. The proof is based on the structure theorem for approximate subgroups proved by Green, Tao and the first author. We also give a…