Related papers: Divisible design Cayley digraphs
The singular cubical homology theory for the category of quivers or digraphs can be constructed similarly to the classical singular homology theory for topological spaces. The case of digraphs and quivers differs from the topological case…
A graph labeling assigns values to the components of a graph (vertices, edges, etc.). In particular, distance magic labelings have been widely studied in undirected graphs. In such a labeling, the vertices are labeled with unique values…
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex…
We give a sufficient and necessary condition for a Praeger-Xu graph to be a Cayley graph.
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…
Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…
A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…
\textit{Minimum distance diagrams}, also known as \textit{\textsf{L}--shapes}, have been used to study some properties related to \textit{weighted Cayley digraphs} of \textit{degree} two and \textit{embedding dimension three numerical…
Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…
The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
From the point of view of discrete geometry, the class of locally finite transitive graphs is a wide and important one. The subclass of Cayley graphs is of particular interest, as testifies the development of geometric group theory. Recall…
The isomorphism problem for digraphs is a fundamental problem in graph theory. This problem for Cayley digraphs has been extensively investigated over the last half a century. In this paper, we consider this problem for $m$-Cayley digraphs…
A set $\mathcal{S}$ of derangements (fixed-point-free permutations) of a set $V$ generates a digraph with vertex set $V$ and arcs $(x,x^\sigma)$ for $x\in V$ and $\sigma\in\mathcal{S}$. We address the problem of characterising those…
We investigate structural and combinatorial properties of Bi-Cayley graphs defined over cyclic groups of order $p^2q^2$, where $p$ and $q$ are distinct primes. We begin by describing their fundamental group-theoretic underpinnings. The main…
In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some…
Suppose G is a finite group, such that |G| = 27p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
An inaccessible, vertex transitive, locally finite graph is described. This graph is not quasi-isometric to a Cayley graph.
This paper considers the degree-diameter problem for extremal and largest known undirected circulant graphs of degree 2 to 9 of arbitrary diameter. As these graphs are vertex transitive it is possible to define their distance partition. The…