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Cycles in the complement of a tree or other graph

F.C. Holroyd, W.J.G. Wingate
<span title="">1985</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Acknowledgment This work arose out of a Combinatorial Research Week, held at the Open University from 26-29 September 1983, and financially supported by the London Mathematical Society and the Mathematics  ...  Faculty of the Open University.  ...  The method used is the inclusionexclusion principle, which has been used before to enumerate cycles, paths and other patterns in the complement of a graph or digraph [2, 9] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(85)80003-0">doi:10.1016/s0012-365x(85)80003-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ytcvizmqlvbmxknujmg4exa6iu">fatcat:ytcvizmqlvbmxknujmg4exa6iu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190313081439/https://core.ac.uk/download/pdf/82755142.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/43/90/4390e03374ee7a8c73b90ebfc31defc4e448d0c8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(85)80003-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Minimum Vector Rank and Complement Critical Graphs [article]

Xiaowei Li, Michael Nathanson, Rachel Phillips
<span title="2013-04-13">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
critical graphs as those for which the removal of any vertex decreases the minimum vector rank of either the graph or its complement.  ...  In addition, this work demonstrates that complement critical graphs form a sufficient set to prove the Graph Complement Conjecture, which remains open.  ...  The authors gratefully acknowledge the support of this program and its many benefits.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1304.3751v1">arXiv:1304.3751v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bmwvavk36venvoqkxusvxys4fa">fatcat:bmwvavk36venvoqkxusvxys4fa</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1304.3751/1304.3751.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1304.3751v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Minimum vector rank and complement critical graphs

Xiaowei Li, Michael Nathanson, Rachel Phillips
<span title="2014-01-01">2014</span> <i title="University of Wyoming Libraries"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/slbuwkwolzbmtmfl2d4oo3gyri" style="color: black;">The Electronic Journal of Linear Algebra</a> </i> &nbsp;
critical graphs as those for which the removal of any vertex decreases the minimum vector rank of either the graph or its complement.  ...  In addition, this work demonstrates that complement critical graphs form a sufficient set to prove the Graph Complement Conjecture, which remains open. http://math.technion.ac.il/iic/ela 2.  ...  The authors gratefully acknowledge the support of this program and its many benefits.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13001/1081-3810.1606">doi:10.13001/1081-3810.1606</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o5oqhcgc25cthoudb2lbdqksdm">fatcat:o5oqhcgc25cthoudb2lbdqksdm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720220924/http://repository.uwyo.edu/cgi/viewcontent.cgi?article=1606&amp;context=ela" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bb/e6/bbe6314a83847de9f506b911616c4fafcdfe98a3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13001/1081-3810.1606"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

A Necessary Condition and a Sufficient Condition for Pairwise Compatibility Graphs

Md. Iqbal Hossain, Sammi Abida Salma, Md. Saidur Rahman, Debajyoti Mondal
<span title="">2017</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
In this paper we give a necessary condition and a sufficient condition for a graph to be a pairwise compatibility graph (PCG). Let G be a graph and let G c be the complement of G.  ...  We show that if G c has two disjoint chordless cycles then G is not a PCG. On the other hand, if G c has no cycle then G is a PCG.  ...  We have shown that if the complement of a given graph G contains two disjoint chordless cycles or two disjoint complements of cycles then G is not a PCG.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00419">doi:10.7155/jgaa.00419</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tiicwihxqjfibcxhvwyrtb5th4">fatcat:tiicwihxqjfibcxhvwyrtb5th4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190308072945/http://pdfs.semanticscholar.org/ef0d/0e54be39d1d04bb65c99699960252fbbf768.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ef/0d/ef0d0e54be39d1d04bb65c99699960252fbbf768.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00419"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Odd-cycle-free facet complexes and the König property

Massimo Caboara, Sara Faridi
<span title="">2011</span> <i title="Rocky Mountain Mathematics Consortium"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/77ppzerlsvfczgvezw53uqeqni" style="color: black;">Rocky Mountain Journal of Mathematics</a> </i> &nbsp;
The original work on higher dimensional trees and cycles was done in the context of commutative algebra, where a rich tradition of studying ideals associated to simplicial complexes was already in place  ...  A much more general notion of a cycle already exists in hypergraph theory ([B1, B2]); we call these hyper-cycles (Definition 5.1) to avoid confusion.  ...  The graph L(∆) is the complement of a 7-cycle (the labels of the facets correspond to those in Figure 1 ). One can verify that ∆ contains no 3, 5, or 7-cycles, so it is odd-cycle-free.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1216/rmj-2011-41-4-1059">doi:10.1216/rmj-2011-41-4-1059</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x6cln5lv3jgnpb5jsioq4s5gfe">fatcat:x6cln5lv3jgnpb5jsioq4s5gfe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809090130/http://www.mscs.dal.ca/~faridi/research/bipartite.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/df/aadf71acab0313d2215d249ff6f8e3687aaea6f4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1216/rmj-2011-41-4-1059"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Counting points of slope varieties over finite fields [article]

Tom Enkosky
<span title="2010-10-12">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The slope variety of a graph is an algebraic set whose points correspond to drawings of a graph. A complement-reducible graph (or cograph) is a graph without an induced four-vertex path.  ...  We construct a bijection between the zeroes of the slope variety of the complete graph on n vertices over F_2, and the complement-reducible graphs on n vertices.  ...  (A k-wheel is a graph formed from a cycle of length k by introducing a new vertex adjacent to all vertices in the cycle.)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1010.1930v2">arXiv:1010.1930v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/42hjtbod75bhtf4cuhbuvwe7yy">fatcat:42hjtbod75bhtf4cuhbuvwe7yy</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1010.1930/1010.1930.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/08/f8/08f800a1ae17c8f038b566a3ad2efd000bd8db01.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1010.1930v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Hamiltonicity of Cubic Cayley Graphs [article]

Henry Glover, Dragan Marusic
<span title="2005-08-31">2005</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
More precisely, it is shown that the Cayley graph X=Cay(G,{a,b,b^-1}) has a Hamilton cycle when |G| (and thus s) is congruent to 2 modulo 4, and has a long cycle missing only two vertices (and thus necessarily  ...  Following a problem posed by Lovász in 1969, it is believed that every connected vertex-transitive graph has a Hamilton path.  ...  The authors wish to thank Yuqing Chen, Marston Conder, Gorazd Lah, Caiheng Li, Klavdija Kutnar, Denis Sjerve, Ron Solomon, and Tsuyi Yang for helpful conversations about the material in this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0508647v1">arXiv:math/0508647v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qpahutxvpnfq3kiju64foyq6ay">fatcat:qpahutxvpnfq3kiju64foyq6ay</a> </span>
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Exploring pairwise compatibility graphs

T. Calamoneri, E. Montefusco, R. Petreschi, B. Sinaimeri
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In particular, we consider the following operations: adding an isolated or universal vertex, adding a pendant vertex, adding a false or a true twin, taking the complement of a graph and taking the disjoint  ...  in the other.  ...  The complement of any cycle C is a PCG. The pairwise compatibility trees of the complement of an odd and even cycle are depicted in Fig. 11 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2012.11.015">doi:10.1016/j.tcs.2012.11.015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sff4ulfbljg7zc37cz22ohqph4">fatcat:sff4ulfbljg7zc37cz22ohqph4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20121114224633/http://wwwusers.di.uniroma1.it/~calamo/PDF-FILES/PCGsetsANDoperations.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f9/80/f980a7c9c26ce0fe8bfe3834a0ac407930fe2284.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2012.11.015"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Cactus Graphs and Graphs Complement Conjecture [article]

Pedro Díaz Navarro
<span title="2018-06-13">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we proof that any cactus graph satisfies graph complement conjecture by finding a orthogonal representation of its complement in R^5.  ...  In other words, G is a C-δ graph if we can label the vertices of G in such a way that (1) the induced graph of the vertices v 1 , v 2 , v 3 in G is either K 3 or P 3 , and (2) for m ≥ 4, the vertex v m  ...  Conclusion Proving GCC + for cactus graph give us other way to prove the result for several families like trees, cycles, chains of cycles, uncyclic graphs, and others which were proved by using combinatorial  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1806.05562v1">arXiv:1806.05562v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h43nnjiydna7bdzg4i7w4n5cki">fatcat:h43nnjiydna7bdzg4i7w4n5cki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191026091647/https://arxiv.org/pdf/1806.05562v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/18/a3/18a383c1a05f6ee3b038c02a5d2f3012a9febec4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1806.05562v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Odd-Cycle-Free Facet Complexes and the König property [article]

Massimo Caboara, Sara Faridi
<span title="2007-03-15">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We use the definition of a simplicial cycle to define an odd-cycle-free facet complex (hypergraph). These are facet complexes that do not contain any cycles of odd length.  ...  This new family of complexes includes the family of balanced hypergraphs, which are known to satisfy the K\"onig property.  ...  The graph L(∆) is the complement of a 7-cycle (the labels of the facets correspond to those in Figure 1 ). One can verify that ∆ contains no 3, 5, or 7-cycles, so it is odd-cycle-free.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0703459v1">arXiv:math/0703459v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fi4qrt3xc5exzl6kr5nfejmmjq">fatcat:fi4qrt3xc5exzl6kr5nfejmmjq</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math0703459/math0703459.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0703459v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Cycles in the complement of a tree

K.B. Reid
<span title="">1976</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
j;xen1. non-endnodes, CMW of which k adjacent to e,uctly two endnodes, ccx%ains fewer cycles than the ~~~trplement of an*) other tree with 11 nodes. provided N > 6.  ...  It is shop n that the complement at the tree with rl nodes and exactly two aC?  ...  The diu-C is the length of a longest path in G. An is a node that is adtjacent to exactly one other node. a graph G will be denoted c.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(76)90082-0">doi:10.1016/0012-365x(76)90082-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2xzohcuunbeyjnymzxik46xzbm">fatcat:2xzohcuunbeyjnymzxik46xzbm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003120852/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/cb3/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDEyMzY1eDc2OTAwODIw.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/99/4f/994fa98f1ecd61dcb2a7548e4a4b7defb31a3bed.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(76)90082-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Some Remarks on Complement of Fuzzy Graphs

Sandeep Narayan
<span title="">2013</span> <i title="IOSR Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b4jiukqriresrjpdbs7dqmv5qi" style="color: black;">IOSR Journal of Mathematics</a> </i> &nbsp;
The complement of fuzzy graphs with a certain structural property is studied in this paper.  ...  In this paper we study the structures of complement of many important fuzzy graphs such as Fuzzy cycles, Blocks etc.  ...  There may be cases when a fuzzy graph will be a fuzzy tree or fuzzy cycle and this structural property may not be inherited by its complement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9790/5728-0747577">doi:10.9790/5728-0747577</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pg457n7hqnhmxogwi6p7brwb4i">fatcat:pg457n7hqnhmxogwi6p7brwb4i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180602091126/http://www.iosrjournals.org/iosr-jm/papers/Vol7-issue4/N0747577.pdf?id=4539" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/22/0c/220c50e56812f0f96359770300b638a47a8d2441.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9790/5728-0747577"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Counting Spanning Trees in Graphs Using Modular Decomposition [chapter]

Stavros D. Nikolopoulos, Leonidas Palios, Charis Papadopoulos
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In particular, when applied on a (q, q − 4)-graph for fixed q, a P4-tidy graph, or a tree-cograph, our algorithm computes the number of its spanning trees in time linear in the size of the graph, where  ...  In this paper we present an algorithm for determining the number of spanning trees of a graph G which takes advantage of the structure of the modular decomposition tree of G.  ...  If every prime graph in T (G) is (i) a spider graph, or (ii) a tree, or (iii) a cycle, or (iv) their complements, or (v) a graph of restricted (fixed) size, then the number of spanning trees of G can be  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-19094-0_21">doi:10.1007/978-3-642-19094-0_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/br67lwkbqjbinogz6p75aggyku">fatcat:br67lwkbqjbinogz6p75aggyku</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829224002/http://www.cs.uoi.gr/~stavros/C-Papers/C-2011-WALCOM.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/22/f6/22f697c4449363c2633592b82a043a8d0237bcfa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-19094-0_21"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Cameron's construction of two-graphs

T. Ishihara
<span title="">2000</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Using this, we give a detailed proof of Cameron's theorem on construction of two-graphs from C-trees. c  ...  Tsaranov and Seidel deÿne a map from trees to two-graphs. Cameron gives another map from C-trees to two-graphs. Covington associates rooted C-trees with N -free graphs.  ...  Let be a graph in the switching class and v 1 v 2 v 3 v 4 a path of length 3 in it. We will prove that some operation of switching yields a graph with some 5-cycle. Take another vertex (v 5 ) of .  ... 
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Graphs whose complement and line graph are isomorphic

Martin Aigner
<span title="">1969</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/57vjscp3tbep5m7txvss2kcz44" style="color: black;">Journal of Combinatorial Theory</a> </i> &nbsp;
It is shown that there are exactly two graphs whose complement and line graph are isomorphic.  ...  GRAPHS WHOSE COMPLEMENT AND LINE GRAPH ARE ISOMORPHIC 275 can have degree at most n --2 in L(G), there must be a tree emanating from every point of C.  ...  This finally implies that all three edges of C have degree exactly n --2 (no edge outside C has degree greater than n --3), and the second graph of Figure l results.  ... 
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