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Switching classes of directed graphs
1986
Journal of combinatorial theory. Series B (Print)
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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
1986
Discrete Mathematics
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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
2016
Mathematical Problems in Engineering
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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
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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]
2017
arXiv
pre-print
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2014 pre-print arXiv:1408.0334v1 fatcat:g5qnzitb35g3vgdxswd6qac7d4
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
2018
Mathematical Problems in Engineering
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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]
2021
arXiv
pre-print
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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
2020
Journal of combinatorial optimization
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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]
2018
arXiv
pre-print
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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]
2005
Lecture Notes in Computer Science
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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]
2010
Lecture Notes in Computer Science
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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]
2017
arXiv
pre-print
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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]
2009
arXiv
pre-print
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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]
2012
arXiv
pre-print
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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
2012
Image Processing & Communications
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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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