Related papers: Higher diameters of Cayley digraphs

A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.

In this paper, we classify reflexible regular Cayley maps for dihedral groups.

This paper discusses some aspects of the history of the Paley graphs and their automorphism groups.

We give a sufficient and necessary condition for a Praeger-Xu graph to be a Cayley graph.

In the present paper, we study Neumaier Cayley graphs. First, we give a criterion for a Cayley graph to be a Neumaier graph with a spread given by the cosets of a subgroup. Further, we construct a new infinite family of Neumaier Cayley…

We address the problem of constructing large undirected circulant networks with given degree and diameter. First we discuss the theoretical upper bounds and their asymptotics, and then we describe and implement a computer-based method to…

Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

In this paper, we first give a new result characterizing the strongly connected digraphs with a diameter equal to that of their line digraphs. Then, we introduce the concepts of the inner diameter and inner radius of a digraph and study…

The aim of this paper is to describe a large class of Hermitian Gray manifolds.

A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a unitary Cayley graph is a coherent algebra. Finally, a class of unitary Cayley graphs that are distance regular are…

In this paper we improve the level and sublevel of algebras obtained by the Cayley-Dickson process when their level and sublevel are greater than dimension of the algebras.

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…

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

A map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Here we generalize that notion to maniplexes and polytopes. We define $\mathcal{M}$ to be a \emph{Cayley extension} of…

The method of higher covariant derivative regularization of gauge theories is reviewed. The objections raised in the literature last years are discussed and the consistency of the method is proven. New approach to regularization of…

This paper investigates the enumeration of Cayley digraphs, focusing on counting Cayley digraphs on dihedral groups up to CI-isomorphism. By leveraging the Cauchy-Frobenius Lemma and properties of automorphisms, we derive an explicit…

Some problems related to the structure of higher terms of the epsilon-expansion of Feynman diagrams are discussed.

A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…