Results 111 to 120 of about 18,169 (133)

On Hamiltonian Property of Cayley Digraphs

Acta Mathematicae Applicatae Sinica, English Series
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Duan, Fang, Huang, Qiong-xiang
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Algebraic degrees of n-Cayley digraphs over abelian groups [PDF]

Journal of Algebraic Combinatorics
A digraph is called an $n$-Cayley digraph if its automorphism group has an $n$-orbit semiregular subgroup. We determine the splitting fields of $n$-Cayley digraphs over abelian groups and compute a bound on their algebraic degrees, before applying our ...
Xiaogang Liu
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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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Connectivity of Cayley Digraphs

1996
The purpose of this chapter is to study several important mathematical problems related to the interconnection structure of networks. Thus the objects of our study are directed and undirected graphs. In many situations it is highly advantageous to use interconnection networks which are highly symmetric.
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Onnectivities of minimal cayley coset digraphs

Applied Mathematics, 1996
The author proves that the connectivity of any minimal Cayley coset digraph coincides with its regular degree. He uses the concept of atoms introduced by \textit{M. E. Watkins} [J. Comb. Theory 8, 23-29 (1970; Zbl 0185.51702)], and, for directed graphs, is due to the reviewer [Combinatorics, Keszthely 1976, Colloq. Math. János Bolyai 18, 193-204 (1978;
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On isomorpisms of Cayley digraphs on dihedral groups

Australas. J Comb., 1997
Let \(G\) be a finite group and \(S\) a subset of \(G\) not containing the identity element 1. The Cayley digraph \(\Gamma=\text{Cay}(G, S)\) is defined by \(V(\Gamma)= G\) and \(E(\Gamma)= \{(g,sg)\mid g\in G, s\in S\}\). A subset \(S\) of \(G\) is called a CI-subset of \(G\), if for any subset \(T\) of \(G\) with \(\text{Cay}(G, S)\) isomorphic to \(\
Haipeng Qu, Jinsong Yu
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Automorphisms of groups and isomophisms of Cayley digraphs

Australas. J Comb., 1995
Let \(G\) be a finite group and \(S\) a subset of \(G\) with \(1\not\in S\). \(D= D(G, S)\) denotes the Cayley digraph of \(G\) with respect to \(S\). Set \(\text{ST}(G, S)= \{\sigma\in \Aut[D(G, S)]\mid \sigma(1)= 1\}\), \(\Aut(G, S)= \{\sigma\in \Aut G\mid \sigma(S)= S\}\), and let \(I\) be the identity permutation on \(G\).
Jixiang Meng, Mingyao Xu
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Isomorphisms and normality of Cayley digraphs of \(A_5\)

Australas. J Comb., 1999
A Cayley digraph \(X= \text{Cay}(G, S)\) is called normal if the right regular representation of \(G\) is a normal subgroup of \(\Aut(X)\). A subset \(S\) is said to be a CI-subset of \(G\), if for any graph isomorphism \(\text{Cay}(G,S)\cong \text{Cay}(G,T)\) there is an \(\alpha\in \Aut(G)\) such that \(S^\alpha= T\).
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Dihedral Butterfly Digraph and Its Cayley Graph Representation

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2008
Yukio Shibata, Yuuki Tanaka
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On isomorphisms of Cayley digraphs on dicyclic groups

Australas. J Comb., 1997
Summary: We prove that for any \(m\in\{1,2,3\}\), the dicyclic group \(B_{4n}\) \((n\neq 2)\) is an \(m\)-DCI group if and only if \(n\) is odd.
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