Results 161 to 170 of about 1,092 (193)

On the Independence Number of Cayley Digraphs of Rectangular Groups

Graphs and Combinatorics, 2018
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Sayan Panma, Nuttawoot Nupo
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Automorphism groups and isomorphisms of Cayley digraphs of Abelian groups [PDF]

Australas. J Comb., 1997
The authors prove that if \(S\) is a minimal generating set of a finite Abelian group \(G\) and the Sylow 2-subgroup of \(G\) is cyclic, then \(S\) and \(S\cup S^{-1}\) are CI-subsets and the corresponding Cayley digraph and graph are normal in the sense that the right regular representation of \(G\) is normal in the group of automorphisms of the graph.
Yan-Quan Feng, Tai-Ping Gao
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Automorphism groups of Cayley digraphs

2008
Let G be a group and S ⊂ G with 1 S. A Cayley digraph Cay(G, S) on G with respect to S is the digraph with vertex set G such that, for x, y ∈ G , there is a directed edge from x to y whenever yx −1 ∈ S.I fS −1 = S, then Cay(G, S) can be viewed as an (undirected) graph by identifying two directed edges (x, y) and ( y, x) with one edge {x, y}.
Ming-Yo Xu, Yan-Quan Feng, Zai-Ping Lu
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On isomorphisms of Cayley digraphs on dicyclic groups [PDF]

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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Extremal Cayley Digraphs of Finite Cyclic Groups

SIAM Journal on Discrete Mathematics, 1995
Let \(\text{Cay}(m, A)\) denote the Cayley digraph of a cyclic group \(\mathbb{Z}_ n\) of residues modulo \(m\) with respect to a generating set \(A\). Let \(r(m, A)\) denote the average distance of \(\text{Cay}(m, A)\), that is \[ r(m, A)= {1\over m} \sum_{x\in \mathbb{Z}_ m} d(0, x), \] where \(d(x, y)\) is the distance from \(x\) to \(y\). For any \(
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The power digraphs associated with generalized dihedral groups

Discrete Mathematics, Algorithms and Applications, 2015
We study the digraphs based on dihedral group [Formula: see text] by using the power mapping, i.e., the set of vertices of these digraphs is [Formula: see text] and the set of edges is [Formula: see text]. These are called the power digraphs and denoted by [Formula: see text]. The cycle and in-degree structure of these digraphs are completely examined.
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Circuits in cayley digraphs of finite abelian groups

Journal of Graph Theory, 1990
AbstractWe find all possible lengths of circuits in Cayley digraphs of two‐generated abelian groups over the two‐element generating sets and over certain three‐element generating sets.
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The automorphism groups of circulant digraphs of degree 3

Ars Comb., 1996
Assume \(S \subseteq Z_n\) and denote by \(C_n(S)\) the digraph with vertices \(Z_n\) and arcs \((i,i+s)\), \(i \in Z_n\), \(s \in S\). Denote by \(L(Z_n)\) the group of translations \(i\to a+i\) and by \(\Omega (S)\) the stabilizer of \(\Aut C_n(S)\) at zero, i.e. \(\Omega (S) = \{\tau \in \Aut C_n(S)\mid \tau (0) = 0\}\).
Qiongxiang Huang, Jinjiang Yuan
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Isomorphisms and automorphism groups of a class of Cayley digraphs on abelian groups [PDF]

Australas. J Comb., 1997
Finite abelian groups are considered. The elements of the cyclic group \(Z_n\) are represented by the integers \(0,1,2,\dots,n- 1\) in appropriate manner. Let \(S\) be a subset of \(Z_n\). Let \(D(S)\) be the difference of the maximal and minimal element of \(S\).
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Cayley Digraphs of Groups

2021
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