Results 41 to 50 of about 18,175 (189)

On the metric dimension of Cayley graphs

AKCE International Journal of Graphs and Combinatorics, 2022
In this paper, we investigate the metric dimension, local metric dimension and edge metric dimension for some (generalized) Cayley graphs.
Afsaneh Rezaei, Kazem Khashyarmanesh, Mojgan Afkhami   +2 more
doaj   +1 more source

Mixed Moore Cayley Graphs [PDF]

Journal of Interconnection Networks, 2017
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 edges and directed arcs in the graph.
openaire   +2 more sources

Ends of groups: a nonstandard perspective

, 2010
We give a nonstandard treatment of the notion of ends of proper geodesic metric spaces. We then apply this nonstandard treatment to Cayley graphs of finitely generated groups and give nonstandard proofs of many of the fundamental results concerning ends ...
Goldbring, Isaac
core   +2 more sources

Characterizing a vertex-transitive graph by a large ball

, 2019
It is well-known that a complete Riemannian manifold M which is locally isometric to a symmetric space is covered by a symmetric space. Here we prove that a discrete version of this property (called local to global rigidity) holds for a large class of ...
de La Salle, Mikael, Sikorav, Jean-Claude, Tessera, Romain   +2 more
core   +2 more sources

A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A₁₁₉

Mathematics, 2021
A Cayley graph Γ=Cay(G,S) is said to be normal if the base group G is normal in AutΓ. The concept of the normality of Cayley graphs was first proposed by M.Y.
Bo Ling, Wanting Li, Bengong Lou
doaj   +1 more source

Large Networks of Diameter Two Based on Cayley Graphs

, 2017
In this contribution we present a construction of large networks of diameter two and of order $\frac{1}{2}d^2$ for every degree $d\geq 8$, based on Cayley graphs with surprisingly simple underlying groups.
BD McKay, G Erskine, J Šiagiová, J Šiagiová, J Šiagiová, J Šiagiová, M Abas, M Abas, P Erdös   +8 more
core   +1 more source

On groups all of whose undirected Cayley graphs of bounded valency are integral

, 2014
A finite group $G$ is called Cayley integral if all undirected Cayley graphs over $G$ are integral, i.e., all eigenvalues of the graphs are integers.
Estélyi, István, Kovács, István
core   +1 more source

Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon T ( q 3 , q ) ${\mathsf{T}}({q}^{3},q)$ in PG ( 7 , q 3 ) ${\mathsf{PG}}(7,{q}^{3})$

Journal of Combinatorial Designs, EarlyView.
ABSTRACT In this paper, we study and characterise the natural embedding of the twisted triality hexagon T ( q 3 , q ) ${\mathsf{T}}({q}^{3},q)$ in PG ( 7 , q 3 ) ${\mathsf{PG}}(7,{q}^{3})$. We begin by describing the possible intersections of subspaces of PG ( 7 , q 3 ) ${\mathsf{PG}}(7,{q}^{3})$ with T ( q 3 , q ) ${\mathsf{T}}({q}^{3},q)$.
Sebastian Petit, Geertrui Van de Voorde
wiley   +1 more source

Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups [PDF]

, 2012
It is shown that distance powers of an integral Cayley graph over an abelian group are again integral Cayley graphs over that group. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral ...
Klotz, W., Sander, T.
core  

Sensitivity and Hamming Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT For any m ≥ 3 $m\ge 3$ we show that the Hamming graph H ( n , m ) $H(n,m)$ admits an imbalanced partition into m $m$ sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong m $m$‐ary Sensitivity Conjecture of Asensio, García‐Marco, and Knauer.
Sara Asensio, Yuval Filmus, Ignacio García‐Marco, Kolja Knauer   +3 more
wiley   +1 more source