Results 91 to 100 of about 18,773 (121)

On the Cayley digraphs that are patterns of unitary matrices

, 2003
This is a short note on some properties of a family of Cayley digraphs. A digraph D is the pattern of a matrix M when D has an arc ij if and only if the ij-th entry of M is nonzero.
Simone, Severini
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A Family of Nonnormal Cayley Digraphs

Acta Mathematica Sinica, English Series, 2001
Let \(G\) be a finite group and \(S\) a generating set of \(G\). The Cayley digraph \(\Gamma=\text{Cay}(G,S)\) is defined by taking \(G\) as set of vertices and the pairs \((g,sg)\), with \(g\in G\) and \(s\in S\), as arcs. The right regular representation \(G_R\) of \(G\) is a subgroup of \(\Aut(\Gamma)\), the automorphisms group of \(\Gamma\).
Feng, Yan Quan, Wang, Dian Jun, Chen, Jing Lin   +2 more
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A Note on Moore Cayley Digraphs

Graphs and Combinatorics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander L. Gavrilyuk, Mitsugu Hirasaka, Vladislav V. Kabanov   +2 more
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Vosperian and superconnected Abelian Cayley digraphs

Graphs and Combinatorics, 1991
A digraph is Vosperian if any fragment has cardinality one or \(| V(X)|-d^ +(X)-1\). A digraph is superconnected if every minimum cutset is the set of vertices adjacent from or to some vertex. The authors use a result of \textit{J. H. B. Kemperman} [Acta Math.
Yahya Ould Hamidoune, Anna S. Lladó, Oriol Serra   +2 more
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On Isomorphisms of Minimal Cayley Graphs and Digraphs

Graphs and Combinatorics, 2001
A Cayley graph or Caylay digraph \(\text{Cay}(G,S)\) is called a CI-graph of the group \(G\) if, for any \(T\subseteq G\), \(\text{Cay}(G,S)\cong \text{Cay}(G,T)\) iff \(S^\sigma= T\) for some \(\sigma\in \text{Aut}(G)\). The aim of the paper is to characterize finite abelian groups for which all minimal Cayley graphs and Cayley digraphs are CI-graphs.
Cai Heng Li, Sanming Zhou
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Some mathematical properties of cayley digraphs with applications to interconnection network design

International Journal of Computer Mathematics, 2005
We consider the relationships between Cayley digraphs and their coset graphs with respect to subgroups and obtain some general results on homomorphism and broadcasting between them.
Behrooz Parhami
exaly   +1 more source

Isomorphisms of Connected Cayley Digraphs

Graphs and Combinatorics, 1998
A Cayley graph \(X(G;S)\) on a finite group \(G\) is said to be a CI-graph if for any \(T\subset G\), \(S=\alpha(T)\) for some \(\alpha\in \Aut(G)\) only when \(X(G;S)\cong X(G;T)\). The author investigates minimal Cayley graphs on abelian groups with respect to being CI-graphs, and isomorphisms of connected Cayley graphs on groups which are abelian ...
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Recognizing Cayley Digraphs

Mathematics Magazine, 2020
A criterion is developed that decides in a finite number of steps whether a finite digraph is a Cayley digraph of some group.
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On Hamiltonian Property of Cayley Digraphs

Acta Mathematicae Applicatae Sinica, English Series
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Duan, Fang, Huang, Qiong-xiang
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On Cayley digraphs on nonisomorphic 2‐groups

Journal of Graph Theory, 2011
AbstractA necessary and sufficient condition is given for two Cayley digraphs X1 = Cay(G1, S1) and X2 = Cay(G2, S2) to be isomorphic, where the groups Gi are nonisomorphic abelian 2‐groups, and the digraphs Xi have a regular cyclic group of automorphisms. Our result extends that of Morris [J Graph Theory 3 (1999), 345–362] concerning p‐groups Gi, where
István Kovács, Mary Servatius
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