Results 71 to 80 of about 994,076 (215)
Barycentric Subdivision of Cayley Graphs With Constant Edge Metric Dimension
IEEE Access, 2020 A motion of a robot in space is represented by a graph. A robot change its position from point to point and its position can be determined itself by distinct labelled landmarks points.
Ali N. A. Koam, A. Ahmad
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Groups with a finite Busemann boundary are virtually cyclic
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric‐functional boundary. We show that if there exists a Cayley graph with finitely many Busemann points, then the underlying group is virtually cyclic.
Corentin Bodart +2 more
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Characterization of subgroup perfect codes in Cayley graphs [PDF]
Discrete Mathematics, 2019 A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code in $\Gamma$ if every vertex of $\Gamma$ is at distance no more than $1$ to exactly one vertex of $C$.
Jiyong Chen, Yanpeng Wang, Binzhou Xia
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Electronic Notes in Discrete Mathematics, 2000 Abstract In this paper we investigate the class of Cayley partitionable graphs. This investigation is motivated by the Strong Perfect Graph Conjecture. Cayley partitionable graphs are Cayley Graphs which are closely related to near-factorizations of finite groups. We prove some structural properties of near-factorizations and give examples of Cayley
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Journal of Combinatorial Designs, Volume 34, Issue 7, Page 306-329, July 2026.ABSTRACT In this paper, we study and characterise the natural embedding of the twisted triality hexagon T ( q 3 , q ) in PG ( 7 , q 3 ). We begin by describing the possible intersections of subspaces of PG ( 7 , q 3 ) with T ( q 3 , q ). Then, we provide conditions on a set of lines ℒ, which ensure that ℒ forms the line set of a naturally embedded ...
Sebastian Petit, Geertrui Van de Voorde
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Normal edge-transitive and $ frac{1}{2}$-arc-transitive Cayley graphs on non-abelian groups of order $2pq$ , $p > q$ are primes [PDF]
International Journal of Group Theory, 2016 Darafsheh and Assari in [Normal edge-transitive Cayley graphs onnon-abelian groups of order 4p, where p is a prime number,Sci. China Math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and$frac{1}{2}-$arc-transitive ...
Ali Reza Ashrafi, Bijan Soleimani
doaj
Unitary Cayley graphs of Dedekind domain quotients
AKCE International Journal of Graphs and Combinatorics, 2016 If X is a commutative ring with unity, then the unitary Cayley graph of X, denoted GX, is defined to be the graph whose vertex set is X and whose edge set is {{a,b}:a−b∈X×}.
Colin Defant
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Discrete Applied Mathematics, 1997 Given a quasigroup \(Q\) with a right identity element and a right-associative generating subset \(S\), a quasi-Cayley graph \(\text{QC}(Q,S)\) is constructed in very much the same way as a Cayley graph is constructed from a given group and a symmetric generating set.
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Complete Rotations in Cayley Graphs
European Journal of Combinatorics, 2001 Consider a Cayley graph \(\text{Cay}(G,S)\) of a finite group \(G\) generated by a set \(S=S^{-1}=\{s_0,\ldots,s_{|S|-1}\}\) where \(1\notin S\). A bijection \(\omega:G\to G\) is called a complete rotation of the graph if \(\omega(1)=1\) and \(\omega(xs_i)=\omega(x)s_{i+1}\) for all \(x\in G\) and all \(i\in{\mathbb{Z}}_{|S|}\).
Marie-Claude Heydemann +2 more
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Representations of Borel Cayley Graphs [PDF]
SIAM Journal on Discrete Mathematics, 1993 Summary: There is a continuing search for dense \((\delta, D)\) interconnection graphs, that is, regular, undirected, degree \(\delta\) graphs with diameter \(D\) and having a large number of nodes. Cayley graphs formed by Borel subgroups currently contribute to some of the densest known \((\delta =4,D)\) graphs for a range of \(D\). However, the group
K. Wendy Tang, Bruce W. Arden
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