Related papers: Semisymmetric cubic graphs of twice odd order
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…
We construct explicity the automorphism group of the folded hypercube $FQ_n$ of dimension $n>3$, as a semidirect product of $N$ by $M$, where $N$ is isomorphic to the Abelian group $Z_2^n$, and $M$ is isomorphic to $Sym(n+1)$, the symmetric…
The general ideal of this paper is to answer the following question: given a numerical property of commuting graphs, a class of semigroups $\mathcal{C}$ and $n\in\mathbb{N}$, is it possible to find a semigroup in $\mathcal{C}$ such that the…
This article provides a method for constructing invariants and semi-invariants of a binary $N$-ic form over a field $k$ characteristics $0$ or $p > N$. A practical and broadly applicable sufficient condition for ensuring nontriviality of…
Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which…
A graph $G = (V, E)$ is said to be word-representable if a word $w$ can be formed using the letters of the alphabet $V$ such that for every pair of vertices $x$ and $y$, $xy \in E$ if and only if $x$ and $y$ alternate in $w$. A…
We introduce a notion of a girth-regular graph as a $k$-regular graph for which there exists a non-descending sequence $(a_1, a_2, \dots, a_k)$ (called the signature) giving, for every vertex $u$ of the graph, the number of girth cycles the…
A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood (resp. in-neighbourhood) of any vertex induces a semicomplete digraph. In this paper, we characterize all…
We introduce $C^*$-algebras associated with directed graphs, along with two generalizations of this concept, namely Exel-Pardo $C^*$-algebras associated with a self-similar action of a group on a directed graph, and the $C^*$-algebras…
For any class $\mathcal{C}$ of bipartite graphs, we define quasi-$\cal C$ to be the class of all graphs $G$ such that every bipartition of $G$ belongs to $\cal C$. This definition is motivated by a generalisation of the switch Markov chain…
We consider diagram groups as defined by V. Guba and M. Sapir. A diagram group G acts on the associated cube complex K by isometries. It is known that if a cube complex L is of a finite dimension then every isometry g of L is semi-simple,…
We introduce the class of network right $*$-abundant semigroups. These are based on networks that extend the notion of a directed graph. This class properly contains the class of graph inverse semigroups. We investigate the structure of…
We call a finite undirected graph minimally k-matchable if it has at least k distinct perfect matchings but deleting any edge results in a graph which has not. An odd subdivision of some graph G is any graph obtained by replacing every edge…
A graph is said to be symmetric if its automorphism group is transitive on its arcs. Guo et al. (Electronic J. Combin. 18, \#P233, 2011) and Pan et al. (Electronic J. Combin. 20, \#P36, 2013) determined all pentavalent symmetric graphs of…
We study topological properties of semi-group actions on the circle by orientation-preserving homeomorhisms. We prove that a generic action either possesses a forward-invariant interval-domain (i.e. a finite union of disjoint circle arcs),…
It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented…
In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups $D_n$, the generalized quaternion groups $Q_n$, the…
For integers $k \geq 2$ and $n \geq k+1$, we prove the following: If $n\cdot k$ is even, there is a connected $k$-regular graph on $n$ vertices. If $n\cdot k$ is odd, there is a connected nearly $k$-regular graph on $n$ vertices.
An infinite linearly ordered set (S,<=) is called doubly homogeneous if its automorphism group A(S) acts 2-transitively on it. We show that any group G arises as outer automorphism group G cong Out(A(S)) of the automorphism group A(S), for…
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…