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### Graphs self-complementary in Kn—e

C.R.J. Clapham
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Graphs self-complementary in K" -e exist for those values of n where self-complementary graphs do not exist.  ...  Graphs selfcomplementary in K" -e in a sense fill the gap where self-complementary graphs do not exist.  ...  For a graph with n vertices, s(G) = n if and only if G is self-complementary. Theorem. If G is self-complementary in K,, -e, then s(G) = n -1. Proof.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(90)90062-m">doi:10.1016/0012-365x(90)90062-m</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jopdieu4f5hupnamai5dghujfa">fatcat:jopdieu4f5hupnamai5dghujfa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190223123031/https://core.ac.uk/download/pdf/82062645.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/11/c4/11c4078d4d2186f5734ef544365395efb24eb82e.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(90)90062-m"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

### Almost self-complementary factors of complete bipartite graphs

Dalibor Fronček
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
An isomorphism qS:Fl ---~F2 is then also called a self-complementin9 isomorphism, or complementing isomorphism and the factors F1 and F2 the self-complementary factors with respect to G or simply the self-complementary  ...  A factor F of a graph G = G(V,E) is a subgraph of G having the same vertex set V.  ...  A complete graph without one edge, kn =K~ -e, is called an almost complete graph.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(96)00237-3">doi:10.1016/s0012-365x(96)00237-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o5ndnts2efdsvnky6u52hqcprm">fatcat:o5ndnts2efdsvnky6u52hqcprm</a> </span>
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### Compressible spaces and $\mathcal{E}\mathcal{Z}$-structures

Craig Guilbault, Molly Moran, Kevin Schreve
<span title="">2021</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
, and graphs of negatively curved or flat Riemannian n-manifolds admit EZ-structures.  ...  We generalize this to higher dimensions by showing that fundamental groups of graphs of closed nonpositively curved Riemannian n-manifolds (each vertex and edge manifold is of dimension n) admit Z-structures  ...  This research was supported in part by Simons Foundation Grant 427244, CRG.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm972-7-2021">doi:10.4064/fm972-7-2021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6rowkvpz2va7rik6lkcml6x57y">fatcat:6rowkvpz2va7rik6lkcml6x57y</a> </span>
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### Page 6468 of Mathematical Reviews Vol. , Issue 96k [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper we define bipartite self-complementary graphs, and show how they can be used to understand the structure of self-complementary graphs.  ...  For G a self-complementary graph of odd order, we describe a decom- position of G into edge disjoint subgraphs, one of which is a bipartite self-complementary graph of order |G|—1.  ...
<span class="external-identifiers"> </span>
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### Indecomposable laplacian integral graphs

Robert Grone, Russell Merris
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
Every decomposable graph is Laplacian integral. i.e., its Laplacian spectrum consists entirely of integers. An indecomposable graph is not decomposable.  ...  A graph that can be constructed from isolated vertices by the operations of union and complement is decomposable.  ...  Thus, apart from K 1 , no decomposable graph is self-complementary (isomorphic to its complement). Can a self-complementary graph be Laplacian integral? Yes, and then some!  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.laa.2007.09.025">doi:10.1016/j.laa.2007.09.025</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7s2d7ocu7rclbbxrej76tyflse">fatcat:7s2d7ocu7rclbbxrej76tyflse</a> </span>
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### Kinetic theory of random graphs: From paths to cycles

E. Ben-Naim, P. L. Krapivsky
<span title="2005-02-28">2005</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
Structural properties of evolving random graphs are investigated.  ...  (A1) Since Ge −G = e z , it is convenient to perform the integration in the complex G plane. In writing the third line, we used dy dG = (1 − G)e −G . FIG. 1 : 1 An evolving random graph.  ...  The large-k behavior of the cycle length distribution is found following the same steps leading to (25) u l,k (t) (8πk 3 ) −1/2 t k e k(1−t) e −l 2 /2k . (40) This distribution is self-similar in the  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.71.026129">doi:10.1103/physreve.71.026129</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/15783400">pmid:15783400</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4rujhlayrdrpj2yeba76szhoa">fatcat:b4rujhlayrdrpj2yeba76szhoa</a> </span>
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### On regular graphs equienergetic with their complements [article]

Ricardo A. Podestá, Denis E. Videla
<span title="2021-05-28">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also characterize all complementary equienergetic pairs of graphs of type 𝒞(2), 𝒞(3) and 𝒞(5) in Cameron's hierarchy (the cases 𝒞(1) and 𝒞(4) are still open).  ...  Next, for the family of strongly regular graphs Γ we characterize all possible parameters srg(n,k,e,d) such that E(Γ) = E(Γ).  ...  Self-complementary graphs are trivially complementary equienergetic, so the interest is put on non self-complementary graphs.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.06378v2">arXiv:2010.06378v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/75makxufenf2naa4xw3zu6s3kq">fatcat:75makxufenf2naa4xw3zu6s3kq</a> </span>
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### Page 7312 of Mathematical Reviews Vol. , Issue 2003j [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “In this paper we prove that the class of self- complementary chordal graphs, the class of self-complementary chordal graphs with 4n vertices, and the class of self- complementary chordal graphs  ...  If F is a bipartite graph with m vertices in one part and k in the other, with minimum degree s > 2, and e > 0 satisfies k > m/e, then ex(F;N) > N2-!/5-© (N> No).  ...
<span class="external-identifiers"> </span>
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### Reinforced concrete beams coated with fiberglass-reinforced polymeric profiles as partial substitutes for the transverse reinforcement

Igor Souza Hoffman, Jorge Henrique Piva, Augusto Wanderlind, Elaine Guglielmi Pavei Antunes
<span title="">2020</span> <i title="FapUNIFESP (SciELO)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5wkjydafg5gmjmgqf65iwki7l4" style="color: black;">Revista IBRACON de Estruturas e Materiais</a> </i> &nbsp;
The results obtained in the tests showed an increase in strength of 83.67% in the beams of group D, and 79.91% for group Q, in relation to the references.  ...  in aggressive environments.  ...  E 1 20 α = .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1590/s1983-41952020000600008">doi:10.1590/s1983-41952020000600008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qlyrepfdvfc37i4637lndneaaa">fatcat:qlyrepfdvfc37i4637lndneaaa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201212164449/http://www.scielo.br/pdf/riem/v13n6/1983-4195-riem-13-6-e13608.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/13/b9/13b9b6882ab26d6ec19a98704a0f843197c59caf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1590/s1983-41952020000600008"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> scielo.br </button> </a>

### Highly dispersed networks by enhanced redirection

Alan Gabel, P. L. Krapivsky, S. Redner
<span title="2013-11-12">2013</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
averaging, and (iii) anomalous scaling, in which N_k, the number of nodes of degree k scales as N_k N^nu-1/k^nu, with 1<nu<2.  ...  mechanism leads to highly-dispersed networks with unusual properties: (i) existence of multiple macrohubs---nodes whose degree is a finite fraction of the total number of network nodes N, (ii) lack of self  ...  For the initial condition of a single node with a self-loop, this star graph contains N − 1 leaves and the hub has degree N + 1.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.88.050802">doi:10.1103/physreve.88.050802</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24329203">pmid:24329203</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gr7ecctjwbbxrmx2r72foebc34">fatcat:gr7ecctjwbbxrmx2r72foebc34</a> </span>
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### Chromatic symmetric functions and H-free graphs [article]

Angèle M. Hamel, Chính T. Hoàng, Jake E. Tuero
<span title="2017-09-11">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Here we extend the claw-free idea to general graphs and consider the e-positivity question for H-free graphs where H = claw, F and H=claw, F, co-F, where F is a four-vertex graph.  ...  Two celebrated conjectures in chromatic symmetric function theory concern the positivity chromatics symmetric functions of claw-free graphs.  ...  to co-claw • P 4 is self-complementary.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.03354v1">arXiv:1709.03354v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ihl2n4iu5vgu7fjxpchnfepwgi">fatcat:ihl2n4iu5vgu7fjxpchnfepwgi</a> </span>
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### Spectral characteristics of network redundancy

Ben D. MacArthur, Rubén J. Sánchez-García
<span title="2009-08-19">2009</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
Here, we use a group-theoretic approach to give a complete description of spectral signatures of redundancy in undirected networks.  ...  Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles.  ...  The first two motifs have complementary spectra while the third is self-complementary.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.80.026117">doi:10.1103/physreve.80.026117</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/19792210">pmid:19792210</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fukwil3x2rd3lgsywy7pqa2hxa">fatcat:fukwil3x2rd3lgsywy7pqa2hxa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200911093926/https://arxiv.org/pdf/0904.3192v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a1/8d/a18d7c8f619a31ef66e8f0faba0e2cf062b068e3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.80.026117"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

### Comparative analysis of normative provisions for seismic design and detailing of reinforced concrete structures

R. A. RODRIGUES, C. E. N. MAZZILLI, T. N. BITTENCOURT
<span title="">2019</span> <i title="FapUNIFESP (SciELO)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5wkjydafg5gmjmgqf65iwki7l4" style="color: black;">Revista IBRACON de Estruturas e Materiais</a> </i> &nbsp;
The parameters for each standard are explained in detail ahead, with the expressions that define the graph curves.  ...  NBR ASCE EUROCODE F x (kN) H x (kN) F x (kN) H x (kN) F x (kN) H x (kN) Rigid soil Table 8 8 Modal participation factors Mode Circular frequency(ω) [rad/s] Period [s] Cyclic  ...  loads additionally to the self-weight; 5.0 kN/m² of accidental overload.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1590/s1983-41952019000500013">doi:10.1590/s1983-41952019000500013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/umlo6fsoj5crfh7jpewd7ox7le">fatcat:umlo6fsoj5crfh7jpewd7ox7le</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200215111759/http://www.scielo.br/pdf/riem/v12n5/1983-4195-riem-12-05-1220.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/4d/41/4d41915b48cff4b92507b79818af99d3900bce43.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1590/s1983-41952019000500013"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> scielo.br </button> </a>

### (-1)-enumeration of plane partitions with complementation symmetry [article]

Theresia Eisenkölbl
<span title="2002-12-11">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For symmetric transpose-complementary and self-complementary plane partitions we get partial results.  ...  We also describe Kuperberg's proof for the case of cyclically symmetric self-complementary plane partitions.  ...  Figure 24 . 24 The graph for cyclically symmetric self-complementary plane partitions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0011175v3">arXiv:math/0011175v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5yixbvhiefhxnpniohqyubnrny">fatcat:5yixbvhiefhxnpniohqyubnrny</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math0011175/math0011175.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/0011175v3" 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>

### Nonequilibrium phase transition in negotiation dynamics

Andrea Baronchelli, Luca Dall'Asta, Alain Barrat, Vittorio Loreto
<span title="2007-11-05">2007</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
Our model displays a non-equilibrium phase transition from an absorbing state in which all agents reach a consensus to an active stationary state characterized either by polarization or fragmentation in  ...  In both cases the universality classes do not seem to depend on the specific interaction topology, the only relevant feature being the total number of different opinions ever present in the system.  ...  Let us consider for definiteness the neutral pair selection strategy, the equation for n k A is in this case dn k A dt = − kn k A k k ′ P (k ′ |k)n k ′ B − kn k A 2 k k ′ P (k ′ |k)n k ′ AB + + 3βkn k  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.76.051102">doi:10.1103/physreve.76.051102</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/18233618">pmid:18233618</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zdyjhoyevnehvltpk6gobrgaqa">fatcat:zdyjhoyevnehvltpk6gobrgaqa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721061204/http://openaccess.city.ac.uk/2667/1/Non-equilibrium%20phase%20transition%20in%20negotiation%20dynamics.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/b2/05/b20503243dcfda3a0316108f7290c10a17b5bf7e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.76.051102"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>
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