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Journal articles on the topic 'Two-graph'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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1

Riera, Constanza, Stéphane Jacob, and Matthew G. Parker. "From graph states to two-graph states." Designs, Codes and Cryptography 48, no. 2 (2008): 179–206. http://dx.doi.org/10.1007/s10623-008-9167-9.

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2

Wafiq, Hibi. "Non-Isomorphism Between Graph And Its Complement." Multicultural Education 7, no. 6 (2021): 256. https://doi.org/10.5281/zenodo.4965942.

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<em>It is known that any graph with six vertices cannot be isomorphic to its complement [3].V. K. Balakrishnan has written in his book Schaum’s solved problems series [1] the following: “Given two arbitrary Simple graphs of the same order and the same size, the problem of determining whetheran isomorphism exists between the two is known as the isomorphism problem in graph theory. In general, itis not all easy (in other words, there is no "efficient algorithm") to solve an arbitrary instance of the isomorphismproblem”, from here came the idea of this paper. As mentioned,isomorphism between two graphs G_1and G_2 is a one-valued function that copies the vertices of graph G_1over all the vertices of graphG_2. If two vertices connected on edge in graphG_1, their imageswill connected on edge in graphG_2;also, if two vertices are not connected in edge on graph G_1 so their images will also not be connected in edge also on graphG_2.The complementary graph of graph G and which will be marked with G ̅, is defined as the graph that contains the same set of vertices, and two vertices connected on edge in graph G will be connected on edge in graph G ̅, and two non-connected vertices on edge in graph G will be non-connected vertices on edge in graphG ̅. The purpose of this paper is to present anenough condition on the vertex number of a given graph so that it is not isomorphic to its complement.</em>

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3

Harary, Frank, and Zsolt Tuza. "Two graph-colouring games." Bulletin of the Australian Mathematical Society 48, no. 1 (1993): 141–49. http://dx.doi.org/10.1017/s0004972700015549.

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4

Ravelo, Jesús N. "Two graph algorithms derived." Acta Informatica 36, no. 6 (1999): 489–510. http://dx.doi.org/10.1007/s002360050182.

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5

Onn, Shmuel. "Two graph isomorphism polytopes." Discrete Mathematics 309, no. 9 (2009): 2934–36. http://dx.doi.org/10.1016/j.disc.2008.07.001.

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6

Nebeský, Ladislav, and Elena Wisztová. "Two edge-disjoint Hamiltonian cycles of powers of a graph." Časopis pro pěstování matematiky 110, no. 3 (1985): 294–301. http://dx.doi.org/10.21136/cpm.1985.118236.

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7

Bacsó, Gabor, Attila Tálos, and Zsolt Tuza. "Graph Domination in Distance Two." Discussiones Mathematicae Graph Theory 25, no. 1-2 (2005): 121. http://dx.doi.org/10.7151/dmgt.1266.

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8

Rho, Yoo-Mi. "ON TWO GRAPH PARTITIONING QUESTIONS." Journal of the Korean Mathematical Society 42, no. 4 (2005): 847–56. http://dx.doi.org/10.4134/jkms.2005.42.4.847.

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9

Kawarabayashi, Ken-ichi, Michael D. Plummer, and Akira Saito. "On two equimatchable graph classes." Discrete Mathematics 266, no. 1-3 (2003): 263–74. http://dx.doi.org/10.1016/s0012-365x(02)00813-0.

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10

Reichenheim, Michael E. "Two-graph Receiver Operating Characteristic." Stata Journal: Promoting communications on statistics and Stata 2, no. 4 (2002): 351–57. http://dx.doi.org/10.1177/1536867x0200200402.

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The command roctg allows visualizing sensitivity (Se)and specificity (Sp) curves according to the range of values of a new diagnostic test, given a “true” state of an event, the reference test. On request, several options for displaying Se and Sp estimates in, or enhancements for, the graphs are also available.

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11

Brtník, Bohumil. "Fully Graph Sensitivity Solution of the Switched Circuits by Two-graph." WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS 20 (September 27, 2021): 252–56. http://dx.doi.org/10.37394/23201.2021.20.28.

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The most general parameter of the electronic circuit is its sensitivity. Sensitivity analysis helps circuit designers to determine boundaries to predict the variations that a particular design variable will generate in a target specifications, if it differs from what is previously assumed. There are two basic methods for calculating the sensitivity: matrix methods and graph methods. The method described in this article is based on a graph, that contains separate input ad output nodes for each phase. This makes it possible to determine the transmission sensitivity even between partial switching phases. The described fully-graph method is suitable for switched current circuits and switched capacitors circuits, too

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12

Kratsch, Stefan, and Pascal Schweitzer. "Graph isomorphism for graph classes characterized by two forbidden induced subgraphs." Discrete Applied Mathematics 216 (January 2017): 240–53. http://dx.doi.org/10.1016/j.dam.2014.10.026.

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13

Proctor, Robert A. "Two Amusing Dynkin Diagram Graph Classifications." American Mathematical Monthly 100, no. 10 (1993): 937. http://dx.doi.org/10.2307/2324217.

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14

Tran, Tuan. "Two problems in graph Ramsey theory." European Journal of Combinatorics 104 (August 2022): 103552. http://dx.doi.org/10.1016/j.ejc.2022.103552.

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15

van der Holst, Hein. "Two Tree-Width-Like Graph Invariants." Combinatorica 23, no. 4 (2003): 633–51. http://dx.doi.org/10.1007/s00493-003-0038-8.

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16

Zhou, H. B. "Two-stage m-way graph partitioning." Parallel Computing 19, no. 12 (1993): 1359–73. http://dx.doi.org/10.1016/0167-8191(93)90081-u.

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17

Godsil, Chris, Maxwell Levit, and Olha Silina. "Graph covers with two new eigenvalues." European Journal of Combinatorics 93 (March 2021): 103280. http://dx.doi.org/10.1016/j.ejc.2020.103280.

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18

Erdös, P. "Two problems in extremal graph theory." Graphs and Combinatorics 2, no. 1 (1986): 189–90. http://dx.doi.org/10.1007/bf01788092.

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19

Van Den Broek, P. M. "Comparison of two graph-rewrite systems." Theoretical Computer Science 61, no. 1 (1988): 67–81. http://dx.doi.org/10.1016/0304-3975(88)90108-9.

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20

Chen, Yuxin, Fangru Lin, Jingyi Huo, and Hui Yan. "Designing Specialized Two-Dimensional Graph Spectral Filters for Spatial-Temporal Graph Modeling." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 11 (2025): 11500–11508. https://doi.org/10.1609/aaai.v39i11.33251.

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Spatial-temporal graph modeling is challenging due to the diverse node interactions across spatial and temporal dimensions. Recent studies typically adopt Graph Neural Networks (GNNs) to perform node-level aggregation at different time steps, acting as a series of low-pass graph spectral filters, for node interaction modeling. However, these filters, confined to the spatial dimension, are ill-suited for processing signals of nodes with inherent spatial-temporal interdependencies. Moreover, oversimplified low-pass filtering fails to fully exploit information from diverse node interactions. To address these issues, we propose a Spatial-Temporal Spectral Graph Neural Network (STSGNN), which designs specialized two-dimensional (2-D) graph spectral filters for comprehensive spatial-temporal graph modeling. First, based on the normalized Laplacian spectrum of spatial and temporal graphs, we extend the existing graph spectral theory from a univariate spatial dimension to a bivariate spatial-temporal dimension through a 2-D Discrete Graph Fourier Transform (2-D DGFT). Then, we leverage the bivariate Bernstein polynomial approximation, with learned basis coefficients, to design 2-D filters with specialized spectral properties for unified spatial-temporal signal filtering. Finally, the filtered signals, with refined spatial-temporal representations, are fed into well-designed pyramidal gated convolution modules to acquire multiple ranges of spatial-temporal dependencies. Experiments on traffic and meteorological prediction tasks demonstrate that STSGNN achieves state-of-the-art performance. Additionally, we visualize the 2-D filters learned from inputs with distinct spatial-temporal characteristics to enhance the model's interpretability.

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21

Abe, Ryuji, Iain R. Aitchison, and Benoît Rittaud. "Two-color Markoff graph and minimal forms." International Journal of Number Theory 12, no. 04 (2016): 1093–122. http://dx.doi.org/10.1142/s1793042116500676.

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Diophantine equations [Formula: see text] and [Formula: see text] are connected with the arithmetic once punctured torus groups having Fricke coordinates [Formula: see text] and [Formula: see text]. We describe and analyze the structure of these equations by a graph, which we call a two-color Markoff graph. The faces of the graph are labeled by matrices in the corresponding once punctured torus group, the word representation of which is easily described owing to arithmetic properties of the graph. As an application, we show that these matrices define Markoff minimal forms attaining the values of the Markoff spectrum given by the positive integer solutions of these equations.

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22

Sudhakar, S., Silviya Francis, and V. Balaji. "Odd mean labeling for two star graph." Applied Mathematics and Nonlinear Sciences 2, no. 1 (2017): 195–200. http://dx.doi.org/10.21042/amns.2017.1.00016.

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AbstractIn this paper further result on odd mean labeling is discussed. We prove that the two star G = K1,m ∧ K1,n is an odd mean graph if and only if |m − n| ≤ 3. The condition for a graph to be odd mean is that p ≤ q + 1, where p and q stands for the number of the vertices and edges in the graph respectively.

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23

Shim, Sooyeon, Junghun Kim, Kahyun Park, and U. Kang. "Accurate graph classification via two-staged contrastive curriculum learning." PLOS ONE 19, no. 1 (2024): e0296171. http://dx.doi.org/10.1371/journal.pone.0296171.

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Given a graph dataset, how can we generate meaningful graph representations that maximize classification accuracy? Learning representative graph embeddings is important for solving various real-world graph-based tasks. Graph contrastive learning aims to learn representations of graphs by capturing the relationship between the original graph and the augmented graph. However, previous contrastive learning methods neither capture semantic information within graphs nor consider both nodes and graphs while learning graph embeddings. We propose TAG (Two-staged contrAstive curriculum learning for Graphs), a two-staged contrastive learning method for graph classification. TAG learns graph representations in two levels: node-level and graph level, by exploiting six degree-based model-agnostic augmentation algorithms. Experiments show that TAG outperforms both unsupervised and supervised methods in classification accuracy, achieving up to 4.08% points and 4.76% points higher than the second-best unsupervised and supervised methods on average, respectively.

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24

Rump, Wolfgang. "Representation theory of two-dimensionalbrauer graph rings." Colloquium Mathematicum 86, no. 2 (2000): 239–51. http://dx.doi.org/10.4064/cm-86-2-239-251.

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25

Simic, Slobodan, and Dragan Stevanovic. "Two shorter proofs in spectral graph theory." Publikacije Elektrotehnickog fakulteta - serija: matematika, no. 14 (2003): 94–98. http://dx.doi.org/10.2298/petf0314094s.

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26

Mao, Yaping, Zhao Wang, and Kinkar Ch Das. "Steiner Degree Distance of Two Graph Products." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 2 (2019): 83–99. http://dx.doi.org/10.2478/auom-2019-0020.

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AbstractThe degree distance DD(G) of a connected graph G was invented by Dobrynin and Kochetova in 1994. Recently, one of the present authors introduced the concept of k-center Steiner degree distance defined as SDD_k (G) = \sum\limits_{\mathop {S \subseteq V(G)}\limits_{\left| S \right| = k} } {\left[ {\sum\limits_{v \in S} {{\it deg} _G (v)} } \right]d_G (S),} where dG(S) is the Steiner k-distance of S and degG(v) is the degree of the vertex v in G. In this paper, we investigate the Steiner degree distance of complete and Cartesian product graphs.

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27

Huh, Young-Sik. "PROJECTIONS OF BOUQUET GRAPH WITH TWO CYCLES." Journal of the Korean Mathematical Society 45, no. 5 (2008): 1341–60. http://dx.doi.org/10.4134/jkms.2008.45.5.1341.

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28

Naeem Kalhoro, Abdul, and Ali Dino Jumani. "A Two-Connected Graph with Gallai’s Property." Advances in Wireless Communications and Networks 5, no. 1 (2019): 29. http://dx.doi.org/10.11648/j.awcn.20190501.14.

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29

Thenge-Mashale, Jyoti Dharmendra, B. Surendranath Reddy, and Rupali Shikharchand Jain. "Comparative study of two Soft Graph Concepts." Global Journal of Pure and Applied Mathematics 20, no. 2 (2024): 241–51. http://dx.doi.org/10.37622/gjpam/20.2.2024.241-251.

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30

Haemers, Willem H., and Elisabeth Kuijken. "The Hermitian two-graph and its code." Linear Algebra and its Applications 356, no. 1-3 (2002): 79–93. http://dx.doi.org/10.1016/s0024-3795(02)00320-8.

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31

Harmer, M. "Two particles on a star graph, I." Russian Journal of Mathematical Physics 14, no. 4 (2007): 435–39. http://dx.doi.org/10.1134/s1061920807040097.

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32

Harmer, M. "Two particles on a star graph, II." Russian Journal of Mathematical Physics 15, no. 4 (2008): 473–80. http://dx.doi.org/10.1134/s1061920808040043.

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33

Teng, Yueyang, Shouliang Qi, Fangfang Han, Lisheng Xu, Yudong Yao, and Wei Qian. "Two graph-regularized fuzzy subspace clustering methods." Applied Soft Computing 100 (March 2021): 106981. http://dx.doi.org/10.1016/j.asoc.2020.106981.

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34

Conlon, David, Jacob Fox, and Benny Sudakov. "On two problems in graph Ramsey theory." Combinatorica 32, no. 5 (2012): 513–35. http://dx.doi.org/10.1007/s00493-012-2710-3.

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35

Klavžar, Sandi. "Two remarks on retracts of graph products." Discrete Mathematics 109, no. 1-3 (1992): 155–60. http://dx.doi.org/10.1016/0012-365x(92)90286-o.

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36

Broersma, H. J., and F. Göbel. "Coloring a graph optimally with two colors." Discrete Mathematics 118, no. 1-3 (1993): 23–31. http://dx.doi.org/10.1016/0012-365x(93)90050-4.

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37

Costa, Eurinardo, Victor Lage Pessoa, Rudini Sampaio, and Ronan Soares. "PSPACE-hardness of Two Graph Coloring Games." Electronic Notes in Theoretical Computer Science 346 (August 2019): 333–44. http://dx.doi.org/10.1016/j.entcs.2019.08.030.

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38

Das, Kinkar Ch, and Muhuo Liu. "On Two Conjectures of Spectral Graph Theory." Bulletin of the Iranian Mathematical Society 44, no. 1 (2018): 43–51. http://dx.doi.org/10.1007/s41980-018-0003-3.

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39

Costa, Eurinardo, Victor Lage Pessoa, Rudini Sampaio, and Ronan Soares. "PSPACE-completeness of two graph coloring games." Theoretical Computer Science 824-825 (July 2020): 36–45. http://dx.doi.org/10.1016/j.tcs.2020.03.022.

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40

Thomason, Andrew. "A Paley-like graph in characteristic two." Journal of Combinatorics 7, no. 2–3 (2016): 365–74. http://dx.doi.org/10.4310/joc.2016.v7.n2.a8.

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41

Eggemann, Nicole, and Steven D. Noble. "The complexity of two graph orientation problems." Discrete Applied Mathematics 160, no. 4-5 (2012): 513–17. http://dx.doi.org/10.1016/j.dam.2011.10.036.

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42

Wang, Hong. "Two vertex-disjoint cycles in a graph." Graphs and Combinatorics 11, no. 4 (1995): 389–96. http://dx.doi.org/10.1007/bf01787818.

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43

Erdós, Paul, Mark Goldberg, János Pach, and Joel Spencer. "Cutting a graph into two dissimilar halves." Journal of Graph Theory 12, no. 1 (1988): 121–31. http://dx.doi.org/10.1002/jgt.3190120113.

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44

Goldschmidt, Olivier, and Alexan Takvorian. "An efficient graph planarization two-phase heuristic." Networks 24, no. 2 (1994): 69–73. http://dx.doi.org/10.1002/net.3230240203.

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45

Matsello, V. V. "Drawings recognition using two-dimensional graph grammars." International Journal of Imaging Systems and Technology 3, no. 3 (1991): 244–48. http://dx.doi.org/10.1002/ima.1850030309.

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46

Shi, Guoyong. "Two-graph analysis of pathological equivalent networks." International Journal of Circuit Theory and Applications 43, no. 9 (2014): 1127–46. http://dx.doi.org/10.1002/cta.1997.

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47

Wang, Hong. "Packing two forests into a bipartite graph." Journal of Graph Theory 23, no. 2 (1996): 209–13. http://dx.doi.org/10.1002/(sici)1097-0118(199610)23:2<209::aid-jgt12>3.0.co;2-b.

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48

Fan, Genghua, and H. A. Kierstead. "Partitioning a graph into two square-cycles." Journal of Graph Theory 23, no. 3 (1996): 241–56. http://dx.doi.org/10.1002/(sici)1097-0118(199611)23:3<241::aid-jgt4>3.0.co;2-s.

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49

Hudson, John F. P. "Distinguishing two graph-encoded manifolds of Lins." Journal of Graph Theory 32, no. 3 (1999): 298–302. http://dx.doi.org/10.1002/(sici)1097-0118(199911)32:3<298::aid-jgt7>3.0.co;2-u.

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50

Bonato, Anthony, and Richard Nowakowski. "Partitioning a graph into two isomorphic pieces." Journal of Graph Theory 44, no. 1 (2003): 1–14. http://dx.doi.org/10.1002/jgt.10121.

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