Related papers: On Neumaier Cayley graphs
In this paper, we study the integral Cayley graphs over a non-abelian group $U_{6n}=\langle a,b\mid a^{2n}=b^3=1, a^{-1}ba=b^{-1}\rangle$ of order $6n$. We give a necessary and sufficient condition for the integrality of Cayley graphs over…
We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show that we construct cospectral Neumaier graphs. Finally, we show…
We establish a necessary and sufficient condition for a normal subgroup of a finite group to be a subgroup perfect code.
Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…
We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained in the sphere. This is achieved by introducing a type of group presentation…
The $(n,k)$-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al.~(Graphs and Combinatorics 2017) and complete…
A regular clique in a regular graph is a clique such that every vertex outside of the clique is adjacent to the same positive number of vertices inside the clique. We continue the study of regular cliques in edge-regular graphs initiated by…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily big finite Heesch number.
We characterize the set of planar locally finite Cayley graphs, and give a finite representation of these graphs by a special kind of finite state automata called labeling schemes. As a result, we are able to enumerate and describe all…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
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…
In this paper, we give a characterization for a class of edge-transitive Cayley graphs, and provide methods for constructing Cayley graphs with certain symmetry properties. Also this study leads to construct and characterise a new family of…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
In this article we complete the work of enumerating typical abelian coverings of Cayley graphs, by reducing the problem to enumerating certain subgroups of finite abelian groups.
The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.
We show that every non-trivial compact connected group and every non-trivial general or special linear group over an infinite field admits a generating set such that the associated Cayley graph has infinite diameter.
In this paper, we introduce the concept of $k$-integral graphs. A graph $\Gamma$ is called $k$-integral if the extension degree of the splitting field of the characteristic polynomial of $\Gamma$ over rational field $\mathbb Q$ is equal to…
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in the problem for mixed graphs, where we allow both undirected…
In this paper, we try to determine exact or bounds on the choosability, or list chromatic numbers of some Cayley graphs, typically some Unitary Cayley graphs and Cayley graphs on Dihedral groups.