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Switching classes of directed graphs

Ying Cheng, Albert L Wells
1986 Journal of combinatorial theory. Series B (Print)  
By analogy with Seidel switching classes of graphs, and two-graphs, this paper develops a theory of switching classes of directed graphs.  ...  The elements of the theory are these: there is a one-to-one correspondence among switching classes of directed graphs, two-digraphs, and cyclic triple covers of the complete digraph.  ...  Not all familiar properties of switching classes of graphs generalized directly to switching classes of digraphs.  ... 
doi:10.1016/0095-8956(86)90075-4 fatcat:paw3xgufubgalbr4z5v3o5njuq

Switching classes of directed graphs and H-equivalent matrices

Ying Cheng
1986 Discrete Mathematics  
In this paper, we define and study the switching classes of directed graphs.  ...  The definition is a generalization of both Van Lint and Seidel's switching classes of graphs and Cameron's switching classes of tournaments.  ...  Switching classes of directed graphs Automorphisms of switching classes Since X is symmetric, we can consider X as the edge set of a graph G(X) with vertex set V.  ... 
doi:10.1016/0012-365x(86)90025-7 fatcat:ukztgklxpjasjpaa3hihxbgwwm

Multiservice Switching Networks with Overflow Links and Resource Reservation

Mariusz Głąbowski, Michał Dominik Stasiak
2016 Mathematical Problems in Engineering  
This paper proposes a new analytical model of a multiservice switching network with overflow links in the first stage and resource reservation for selected call classes in output directions.  ...  The proposed model assumes that both the overflow mechanism and the resource reservation mechanism can be used in a number of selected, or all, classes of calls.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2016/4090656 fatcat:5ukqglosdbdqbfjwdtg4b2rvam

Page 44 of Mathematical Reviews Vol. , Issue 80A [page]

1980 Mathematical Reviews  
An automorphism group of a switch- ing class (a group of permutations of the vertex set permuting among themselves the graphs in the class) may or may not fix a graph in the class.  ...  Relation by switching is an equivalence relation on the class of graphs with given vertex set.  ... 

Complex Two-Graphs via Equiangular Tight Frames [article]

Thomas Hoffman, James Solazzo
2017 arXiv   pre-print
In 'A survey of two-graphs' Sei, J.J. Seidel lays out the connections between simple graphs, two-graphs, equiangular lines and strongly regular graph.  ...  This article gives a generalization of two-graphs for which these connections can be mimicked using roots of unity beyond ± 1.  ...  On 3 vertices there are 4 non-isomorphic graphs, 2 distinct switching classes of graphs, and 2 distinct switching equivalent classes of graphs.  ... 
arXiv:1408.0334v2 fatcat:tr2dsnxud5d23ghlmdncgrp6yq

Distributed Consensus Design for a Class of Uncertain Linear Multiagent Systems under Unbalanced Randomly Switching Directed Topologies

Dinh Hoa Nguyen
2018 Mathematical Problems in Engineering  
The appealing features of this approach are as follows. First, it uses the mildest assumption for the randomly switching topologies that the union of switched graphs has a spanning tree.  ...  This paper proposes a novel approach to design fully distributed consensus controllers for heterogeneous linear Multiagent Systems subjected to randomly switching directed topologies and model uncertainties  ...  Theorem 4 provides a powerful consensus design for (i) the most general class of randomly switching graphs where none of them or their union is balanced; (ii) a class of heterogeneous uncertain linear  ... 
doi:10.1155/2018/8081264 fatcat:43rtx7mhc5djdbwdak2ywuwh6e

Switching equivalence of Hermitian adjacency matrix of mixed graphs [article]

Monu Kadyan, Bikash Bhattacharjya
2021 arXiv   pre-print
We find bounds on the number of switching equivalence classes of all mixed graphs with the same underlying graph.  ...  We also discuss the action of automorphism group of a graph on switching equivalence classes.  ...  Switching equivalence is an equivalence relation on M(G). An equivalence class under this switching equivalence is a switching equivalence class of mixed graphs.  ... 
arXiv:2103.13632v1 fatcat:n36arszilvd2lk2q45b7jmnimi

On characterizations for subclasses of directed co-graphs

Frank Gurski, Dominique Komander, Carolin Rehs
2020 Journal of combinatorial optimization  
By transmitting the restrictions of undirected subclasses to the directed classes, we define the corresponding subclasses for directed co-graphs.  ...  Until now, there are only a few versions of subclasses of directed co-graphs.  ...  This class is not very useful for our directed co-graph hierarchy, as they are incomparable to most of the graph classes in it, though it is a superclass of directed threshold graphs (see Sect. 4.17)  ... 
doi:10.1007/s10878-020-00670-5 fatcat:4t6ezwtrxrdvfmz5ujzw2fo5zm

Smaller Universes for Uniform Sampling of 0,1-matrices with fixed row and column sums [article]

Annabell Berger, Corrie Jacobien Carstens
2018 arXiv   pre-print
We prove that ignoring node labels corresponds to projecting a Markov chain onto equivalence classes of isomorphic graphs and that the resulting projected Markov chain converges to its stationary distribution  ...  This article focusses on Markov chain approaches for sampling, where a close-to-random graph is produced by applying a large number N of small changes to a given graph.  ...  Acknowledgement The authors would like to thank Pieter Kleer for insightful comments and discussions on the content of this work.  ... 
arXiv:1803.02624v3 fatcat:y4ogvx3rxbgi5bqd4ontkrlfju

An Adaptive Genetic Algorithm for the Minimal Switching Graph Problem [chapter]

Maolin Tang
2005 Lecture Notes in Computer Science  
Minimal Switching Graph (MSG) is a graph-theoretic representation of the constrained via minimization problem -a combinatorial optimization problem in integrated circuit design automation.  ...  From a computational point of view, the problem is NP-complete.  ...  Minimal Switching Graph Problem A directed bigraph is a directed graph whose vertices can be partitioned into two disjoint sets such that no vertices within the same set are adjacent.  ... 
doi:10.1007/978-3-540-31996-2_21 fatcat:lr5tjp2ndndhhgycc7oioeszyi

Uniform Sampling of Digraphs with a Fixed Degree Sequence [chapter]

Annabell Berger, Matthias Müller-Hannemann
2010 Lecture Notes in Computer Science  
The first uses an additional operation (a reorientation of induced directed 3-cycles) which makes the state graph strongly connected, the second selects randomly one of the isomorphic components and samples  ...  We also explain in this paper that a popular switching algorithm fails in general to sample uniformly at random because the state graph of the Markov chain decomposes into different isomorphic components  ...  Roughly speaking, this class consists of induced directed 3-cycles C i formed by triples  ... 
doi:10.1007/978-3-642-16926-7_21 fatcat:dhs46s4unzfdlnxhhk3mccgtwy

On Perfect Matchings in Matching Covered Graphs [article]

Jinghua He, Erling Wei, Dong Ye, Shaohui Zhai
2017 arXiv   pre-print
graph of class 1 is always switching-equivalent to either ∅ or E(G)?  ...  In this paper, we show that, for every integer k> 3, there exist infinitely many k-regular graphs of class 1 with an arbitrarily large equivalent class K such that K is not switching-equivalent to either  ...  Hence G(k, m) is a k-regular non-bipartite graph of class 1 which has a non-feasible set X not switching-equivalent to ∅ or E(G(k, m)).  ... 
arXiv:1703.05412v2 fatcat:yunkqjonozbszm37ttxsuunzt4

On uniform sampling simple directed graph realizations of degree sequences [article]

M. Drew Lamar
2009 arXiv   pre-print
It has been shown in the past that one can perform a Markov chain arc-switching algorithm to sample a simple directed graph uniformly by performing two types of switches: a 2-switch and a directed 3-cycle  ...  In particular, the class of degree sequences where this is required is a subclass of the directed 3-cycle anchored degree sequences.  ...  This work was funded by the postdoctoral and undergraduate biological sciences education program grant awarded to the College of William and Mary by the Howard Hughes Medical Institute.  ... 
arXiv:0912.3834v1 fatcat:btygwyiiljdwdemtxh4idkcl4a

The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs [article]

Felix Canavoi, Erich Grädel, Roman Rabinovich
2012 arXiv   pre-print
We analyse the examples provided by Friedmann in terms of complexity measures for directed graphs such as treewidth, DAG-width, Kelly-width, entanglement, directed pathwidth, and cliquewidth.  ...  It is known that for every class of parity games on which one of these parameters is bounded, the winning regions can be efficiently computed.  ...  This makes all values of measures that describe cyclicity (i.e., treewidth, directed pathwidth, DAG-width, and Kelly-width) unbounded on the class of the counterexample graphs, but cliquewidth of the graphs  ... 
arXiv:1210.2459v1 fatcat:vptg3s37n5d3lnwvlsguo7faem

Internal Blocking Probability Calculation in Switching Networks with Additional Inter-Stage Links and Mixture of Erlang and Engset Traffic

Mariusz Gła̧bowski, Michał Dominik Stasiak
2012 Image Processing & Communications  
The method can be used for blocking probability calculation in switching networks that are offered multi-service traffic generated by finite and infinite number of sources, i.e., in switching networks  ...  The simulation study performed proves high accuracy of the method proposed and confirms the correctness and validity of all adopted theoretical assumptions.  ...  -effective availability for the stream of class c in the equivalent network, • π(c) -probability of direct non-availability [3, 24] of the switch of the last stage for calls of class c, • k -the number  ... 
doi:10.2478/v10248-012-0016-0 fatcat:2tfpev3nk5hkjfgvzo5whakllq
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