Results 101 to 110 of about 9,039,686 (137)

Line Digraph Iterations and the (d, k) Digraph Problem

IEEE Transactions on Computers, 1984
This paper studies the behavior of the diameter and the average distance between vertices of the line digraph of a given digraph. The results obtained are then applied to the so-called (d, k) digraph problem, that is, to maximize the number of ...
Fiol Mora, Miquel Àngel, Alegre de Miguel, Ignacio, Andrés Yebra, José Luis   +2 more
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Extremal Cayley Digraphs of Finite Abelian Groups

2011 14th IEEE International Conference on Computational Science and Engineering, 2011
Cayley graphs of finite abelian groups are often used to model communication networks. Because of their applications, extremal Cayley digraphs have been studied extensively in recent years. Given any positive integers d and k. Let m∗(d, k) denote the largest positive integer m such that there exists an m-element finite abelian group Γ and a kelement ...
Abby Gail Mask, Joni Schneider, Xingde Jia   +2 more
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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 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 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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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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Automorphism groups and isomorphisms of Cayley digraphs of Abelian groups

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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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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On circulant digraphs with regular automorphism groups

Applied Mathematics, 1996
Let \(G\) be a finite group. Especially, we denote the cyclic group of order \(n (\geq 3)\) by \(Z_n\). A finite simple directed graph \(H\) is called a directed graphical regular representation (abbreviated as DRR) of \(G\) if (i) the automorphism group of \(H\) is isomorphic to \(G\) and (ii) whenever \((u,v)\) is an ordered pair consisting of ...
Meng, Jixiang, Dong, Yali
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