Directed cycles with chords

AbstractWe consider the directed graph representing the obstruction relation between objects moving along the streamlines of a two-dimensional velocity field. A collection of objects is sequentially separable if and only if the corresponding graph has no directed cycles. A sufficient condition for this is the permeability of closed Jordan curves.

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Cooperative Salvo Guidance Using Finite-Time Consensus Over Directed Cycles

IEEE Transactions on Aerospace and Electronic Systems ◽

10.1109/taes.2019.2934675 ◽

2020 ◽

Vol 56 (2) ◽

pp. 1504-1514 ◽

Cited By ~ 5

Author(s):

Shashi Ranjan Kumar ◽

Dwaipayan Mukherjee

Keyword(s):

Finite Time ◽

Directed Cycles

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Algebraic Algorithms for Even Circuits in Graphs

Mathematics ◽

10.3390/math7090859 ◽

2019 ◽

Vol 7 (9) ◽

pp. 859

Author(s):

Huy Tài Hà ◽

Susan Morey

Keyword(s):

Algebraic Algorithms ◽

Directed Cycles

We present an algebraic algorithm to detect the existence of and to list all indecomposable even circuits in a given graph. We also discuss an application of our work to the study of directed cycles in digraphs.

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K-domination number of products of two directed cycles and two directed paths

International Journal of Computing Science and Mathematics ◽

10.1504/ijcsm.2018.091734 ◽

2018 ◽

Vol 9 (2) ◽

pp. 197

Author(s):

Ramy Shaheen

Keyword(s):

Domination Number ◽

Directed Paths ◽

Directed Cycles

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Balanced directed cycle designs based on cyclic groups

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700038246 ◽

1995 ◽

Vol 58 (2) ◽

pp. 210-218 ◽

Cited By ~ 1

Author(s):

Chaufah Nilrat ◽

Cheryl E. Praeger

Keyword(s):

Directed Graph ◽

Cyclic Group ◽

Complete Classification ◽

Directed Cycle ◽

Group Of Automorphisms ◽

Edge Disjoint ◽

Cyclic Groups ◽

Directed Cycles

AbstractA balanced directed cycle design with parameters (υ, k, 1), sometimes called a (υ, k, 1)-design, is a decomposition of the complete directed graph into edge disjoint directed cycles of length k. A complete classification is given of (υ, k, 1)-designs admitting the holomorph {øa, b: x ↦ ax + b∣ a, b ∈ Zυ, (a, υ1) = 1} of the cyclic group Zυ as a group of automorphisms. In particular it is shown that such a design exists if and ony if one of (a) k = 2, (b) p ≡ 1 (mod k) for each prime p dividing υ, or (c) k is the least prime dividing υ, k2 does not divide υ, and p ≡ 1 (mod k) for each prime p < k dividing υ.

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On the Study of Transience and Recurrence of the Markov Chain Defined by Directed Weighted Circuits Associated with a Random Walk in Fixed Environment

Journal of Probability and Statistics ◽

10.1155/2013/424601 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 2

Author(s):

Chrysoula Ganatsiou

Keyword(s):

Markov Chain ◽

Random Walk ◽

Representation Theory ◽

Markov Processes ◽

Directed Cycles

By using the cycle representation theory of Markov processes, we investigate proper criterions regarding transience and recurrence of the corresponding Markov chain represented uniquely by directed cycles (especially by directed circuits) and weights of a random walk with jumps in a fixed environment.

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