Orthogonal embeddings of graphs in Euclidean space by Wai Chee Shiu, Richard M. Low

“…We also determine the orthogonal ranks for cycles, complete bipartite graphs, one-point union of two graphs, Cartesian product of orthogonal graphs, bicyclic graphs without pendant, and tessellation graphs.…”
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Independent Roman Domination: The Complexity and Linear-Time Algorithm for Trees by Zhixing Duan, Huiqin Jiang, Xinyue Liu, Pu Wu, Zehui Shao

“…In this paper, we prove that the decision problem of minimum IRDF is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>P</mi></mrow></semantics></math></inline-formula>-complete for chordal bipartite graphs. Then, we research the difference in complexity between the decision problem of RDF and IRDF. …”
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Analysis of approximation and uncertainty in optimization by Mastin, Dana Andrew

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Some problems in Graph Ramsey Theory by Grinshpun, Andrey Vadim

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Graph polynomial associated to some graphs of certain finite nonabelian groups by Najmuddin, Nabilah

“…All these graphs are found and expressed in general in the form of the union and join of some complete graphs, complete bipartite graphs, and also complete multipartite graphs. …”
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A reverse Sidorenko inequality by Sah, Ashwin, Sawhney, Mehtaab, Stoner, David, Zhao, Yufei

“…For 2-spin Ising models, our results give a complete characterization of extremal graphs: complete bipartite graphs maximize the partition function of 2-spin antiferromagnetic models and cliques maximize the partition function of ferromagnetic models. …”
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Method of information technology for structure analysis of urban network fire-rescue units by Svitlana Danshyna, Artem Nechausov

“…The study of the classical location problem and its adaptation to real problems arising from the analysis of the urban network of fire-rescue units made it possible to represent it as a set of independent complete bipartite graphs. To search the location of network nodes while solving an adapted problem, an IT method is developed, which, based on the p-median model, combines the author’s methodology for studying information processes and methods of geospatial analysis. …”
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Bridging Theory and Practice in Parallel Clustering by Shi, Jessica

“…We address bi-core decomposition and butterfly peeling, which are specialized algorithms for bipartite graphs, and we study k-clique peeling and nucleus decomposition, which generalize classic decomposition algorithms to higher order structures. …”
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On the analysis of complex networks : fundamental limits, scalable algorithms, and applications by Feizi, Soheil

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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees by Xinyue Liu, Huiqin Jiang, Pu Wu, Zehui Shao

“…In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>t</mi><mo stretchy="false">{</mo><mi>R</mi><mn>3</mn><mo stretchy="false">}</mo></mrow></msub></semantics></math></inline-formula> for trees.…”
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Algorithms and algorithmic obstacles for probabilistic combinatorial structures by Li, Quan, Ph. D. Massachusetts Institute of Technology

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Constant Sum Group Flows of Graphs by Tao-Ming Wang

“…We determine the magic sum spectrum of complete bipartite graphs <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msub></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>≥</mo><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula> as the additive cyclic subgroups of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>k</mi></msub></semantics></math></inline-formula> generated by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mi>k</mi><mi>d</mi></mfrac></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mi>g</mi><mi>c</mi><mi>d</mi><mo>(</mo><mi>m</mi><mo>−</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Total Roman {3}-domination in Graphs by Zehui Shao, Doost Ali Mojdeh, Lutz Volkmann

“…Finally, we investigate the complexity of total Roman <inline-formula> <math display="inline"> <semantics> <mrow> <mo>{</mo> <mn>3</mn> <mo>}</mo> </mrow> </semantics> </math> </inline-formula>-domination for bipartite graphs.…”
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