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Switching classes of directed graphs

1986
*
Journal of combinatorial theory. Series B (Print)
*

By analogy with Seidel

doi:10.1016/0095-8956(86)90075-4
fatcat:paw3xgufubgalbr4z5v3o5njuq
*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. ...##
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Switching classes of directed graphs and H-equivalent matrices

1986
*
Discrete Mathematics
*

In this paper, we define and study the

doi:10.1016/0012-365x(86)90025-7
fatcat:ukztgklxpjasjpaa3hihxbgwwm
*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. ...##
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Multiservice Switching Networks with Overflow Links and Resource Reservation

2016
*
Mathematical Problems in Engineering
*

This paper proposes a new analytical model

doi:10.1155/2016/4090656
fatcat:5ukqglosdbdqbfjwdtg4b2rvam
*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. ...##
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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]

2017
*
arXiv
*
pre-print

In 'A survey

arXiv:1408.0334v2
fatcat:tr2dsnxud5d23ghlmdncgrp6yq
*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*. ...##
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Distributed Consensus Design for a Class of Uncertain Linear Multiagent Systems under Unbalanced Randomly Switching Directed Topologies

2018
*
Mathematical Problems in Engineering
*

The appealing features

doi:10.1155/2018/8081264
fatcat:43rtx7mhc5djdbwdak2ywuwh6e
*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 ...##
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Switching equivalence of Hermitian adjacency matrix of mixed graphs
[article]

2021
*
arXiv
*
pre-print

We find bounds on the number

arXiv:2103.13632v1
fatcat:n36arszilvd2lk2q45b7jmnimi
*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*. ...##
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On characterizations for subclasses of directed co-graphs

2020
*
Journal of combinatorial optimization
*

By transmitting the restrictions

doi:10.1007/s10878-020-00670-5
fatcat:4t6ezwtrxrdvfmz5ujzw2fo5zm
*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) ...##
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Smaller Universes for Uniform Sampling of 0,1-matrices with fixed row and column sums
[article]

2018
*
arXiv
*
pre-print

We prove that ignoring node labels corresponds to projecting a Markov chain onto equivalence

arXiv:1803.02624v3
fatcat:y4ogvx3rxbgi5bqd4ontkrlfju
*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. ...##
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An Adaptive Genetic Algorithm for the Minimal Switching Graph Problem
[chapter]

2005
*
Lecture Notes in Computer Science
*

Minimal

doi:10.1007/978-3-540-31996-2_21
fatcat:lr5tjp2ndndhhgycc7oioeszyi
*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. ...##
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Uniform Sampling of Digraphs with a Fixed Degree Sequence
[chapter]

2010
*
Lecture Notes in Computer Science
*

The first uses an additional operation (a reorientation

doi:10.1007/978-3-642-16926-7_21
fatcat:dhs46s4unzfdlnxhhk3mccgtwy
*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 ...##
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On Perfect Matchings in Matching Covered Graphs
[article]

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)). ...

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

2009
*
arXiv
*
pre-print

It has been shown in the past that one can perform a Markov chain arc-

arXiv:0912.3834v1
fatcat:btygwyiiljdwdemtxh4idkcl4a
*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. ...##
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The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs
[article]

2012
*
arXiv
*
pre-print

We analyse the examples provided by Friedmann in terms

arXiv:1210.2459v1
fatcat:vptg3s37n5d3lnwvlsguo7faem
*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*...##
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Internal Blocking Probability Calculation in Switching Networks with Additional Inter-Stage Links and Mixture of Erlang and Engset Traffic

2012
*
Image Processing & Communications
*

The method can be used for blocking probability calculation in

doi:10.2478/v10248-012-0016-0
fatcat:2tfpev3nk5hkjfgvzo5whakllq
*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 ...
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