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Journal articles on the topic 'Graph drawing'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

EADES, PETER, XUEMIN LIN, and ROBERTO TAMASSIA. "AN ALGORITHM FOR DRAWING A HIERARCHICAL GRAPH." International Journal of Computational Geometry & Applications 06, no. 02 (1996): 145–55. http://dx.doi.org/10.1142/s0218195996000101.

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Hierarchical graphs appear in several graph drawing applications, where nodes are assigned layers for semantic reasons. More importantly, general methods for drawing directed graphs usually begin by transforming the input digraph into a hierarchical graph, then applying a hierarchical graph drawing algorithm. This paper introduces the Degree Weighted Barycentre (DWB) algorithm for drawing hierarchical graphs. We show that drawings output by DWB satisfy several important aesthetic criteria: under certain connectivity conditions, they are planar, convex, and symmetric whenever such drawings are

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2

BRIDGEMAN, STINA, ASHIM GARG, and ROBERTO TAMASSIA. "A GRAPH DRAWING AND TRANSLATION SERVICE ON THE WORLD WIDE WEB." International Journal of Computational Geometry & Applications 09, no. 04n05 (1999): 419–46. http://dx.doi.org/10.1142/s021819599900025x.

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Both practitioners and researchers can take better advantage of the latest developments in graph drawing if implementations of graph drawing algorithms are made available on the WWW. We envision a graph drawing and translation service for the WWW with dual objectives: drawing user-specified graphs, and translating graph-descriptions and graph drawings from one format to another. As a first step toward realizing this vision, we have developed a prototype service which is available at .

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3

Iqbal Hossain, Md, and Md Saidur Rahman. "Straight-line monotone grid drawings of series–parallel graphs." Discrete Mathematics, Algorithms and Applications 07, no. 02 (2015): 1550007. http://dx.doi.org/10.1142/s179383091550007x.

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A monotone drawing of a planar graph G is a planar straight-line drawing of G where a monotone path exists between every pair of vertices of G in some direction. Recently monotone drawings of graphs have been discovered as a new standard for visualizing graphs. In this paper we study monotone drawings of series–parallel graphs in a variable embedding setting. We show that a series–parallel graph of n vertices has a straight-line planar monotone drawing on a grid of size O(n) × O(n2) and such a drawing can be found in linear time.

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4

Dib, Fadi K., and Peter Rodgers. "Graph drawing using Jaya." PLOS ONE 18, no. 6 (2023): e0287744. http://dx.doi.org/10.1371/journal.pone.0287744.

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Graph drawing, involving the automatic layout of graphs, is vital for clear data visualization and interpretation but poses challenges due to the optimization of a multi-metric objective function, an area where current search-based methods seek improvement. In this paper, we investigate the performance of Jaya algorithm for automatic graph layout with straight lines. Jaya algorithm has not been previously used in the field of graph drawing. Unlike most population-based methods, Jaya algorithm is a parameter-less algorithm in that it requires no algorithm-specific control parameters and only po

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5

Kang, Ming-Hsuan, and Jing-Wen Gu. "Toroidal Spectral Drawing." Axioms 11, no. 3 (2022): 137. http://dx.doi.org/10.3390/axioms11030137.

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We give a deterministic drawing algorithm to draw a graph onto a torus, which is based on the usual spectral drawing algorithm. For most of the well-known toroidal vertex-transitive graphs, the result drawings give an embedding of the graphs onto the torus.

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6

BIEDL, THERESE C., BRENDAN P. MADDEN, and IOANNIS G. TOLLIS. "THE THREE-PHASE METHOD: A UNIFIED APPROACH TO ORTHOGONAL GRAPH DRAWING." International Journal of Computational Geometry & Applications 10, no. 06 (2000): 553–80. http://dx.doi.org/10.1142/s0218195900000310.

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In this paper, we study orthogonal graph drawings from a practical point of view. Most previously existing algorithms restricted the attention to graphs of maximum degree four. Here we study orthogonal drawing algorithms that work for any input graph, and discuss different models for such drawings. Then we introduce the three-phase method, a generic technique to create high-degree orthogonal drawings. This approach simplifies the description and implementation of orthogonal graph drawing, and can be applied to global as well as interactive and incremental settings.

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7

Binucci, Carla, Aaron Büngener, Giuseppe Di Battista, et al. "Min-$k$-planar Drawings of Graphs." Journal of Graph Algorithms and Applications 28, no. 2 (2024): 1–35. http://dx.doi.org/10.7155/jgaa.v28i2.2925.

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The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing. One of the most studied types of drawings in this area are the $k$-planar drawings $(k \geq 1)$, where each edge cannot cross more than $k$ times. We generalize $k$-planar drawings, by introducing the new family of min-$k$-planar drawings. In a min-$k$-planar drawing edges can cross an arbitrary number of times, but for any two crossing edges, one of the two must have no more than $k$ crossings. We prove a general uppe

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YELTEKİN ATAR, Betül Şeyma, and Işıl AYKUTLU. "High School Students’ User Skills Concerning Force and Motion Graphs." Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi 43, no. 1 (2023): 211–42. http://dx.doi.org/10.17152/gefad.1205369.

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In this study, the aim was to examine Year 11 students’ skills of reading-interpreting and drawing graphs of force and motion and to lay bare the relationship between graph reading-interpretation and drawing graphs. Conducted in the survey model, the study was realised with the participation of 209 Year 11 students studying at Anatolian high schools in Ankara. Graph Reading and Interpretation Skills Test (GRIST) which includes 13 multiple-choice items and Graph Drawing Skills Form (GDSF) which includes 5 open-ended items were used as data collection tools. At the end of the study, it was deter

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9

Bertolazzi, P., G. Di Battista, and G. Liotta. "Parametric graph drawing." IEEE Transactions on Software Engineering 21, no. 8 (1995): 662–73. http://dx.doi.org/10.1109/32.403790.

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10

DEHKORDI, HOOMAN REISI, and PETER EADES. "EVERY OUTER-1-PLANE GRAPH HAS A RIGHT ANGLE CROSSING DRAWING." International Journal of Computational Geometry & Applications 22, no. 06 (2012): 543–57. http://dx.doi.org/10.1142/s021819591250015x.

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There is strong empirical evidence that human perception of a graph drawing is negatively correlated with the number of edge crossings. However, recent experiments show that one can reduce the negative effect by ensuring that the edges that cross do so at large angles. These experiments have motivated a number of mathematical and algorithmic studies of “right angle crossing (RAC)” drawings of graphs, where the edges cross each other perpendicularly. In this paper we give an algorithm for constructing RAC drawings of “outer-1-plane” graphs, that is, topological graphs in which each vertex appea

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11

Angelini, Patrizio, Steven Chaplick, Sabine Cornelsen, and Giordano Da Lozzo. "On Upward-Planar L-Drawings of Graphs." Journal of Graph Algorithms and Applications 28, no. 1 (2024): 275–99. http://dx.doi.org/10.7155/jgaa.v28i1.2950.

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In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge $e=(v,w)$ is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail $v$ of $e$ and of a horizontal segment ending at the head $w$ of $e$. Distinct edges may overlap, but must not cross. Recently, upward-planar L-drawings have been studied for $st$-graphs, i.e., planar DAGs with a single source $s$ and a single sink $t$ containing an edge directed from $s$ to $t$. It is known that a plane $st$-graph, i.e., an embedded $st$-graph in which the edge $(s,t)$ is incident to the outer face

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12

Liotta, Giuseppe, and Henk Meijer. "Advances in graph drawing: The 11th International Symposium on Graph Drawing." Discrete Applied Mathematics 155, no. 9 (2007): 1077. http://dx.doi.org/10.1016/j.dam.2006.10.002.

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13

A. Antony mary, A., A. Amutha, and M. S. Franklin Thamil Selvi. "A Study on Slope Number of Certain Classes of Bipartite Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 440. http://dx.doi.org/10.14419/ijet.v7i4.10.21036.

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Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs crea

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DUNCAN, CHRISTIAN A., ALON EFRAT, STEPHEN KOBOUROV, and CAROLA WENK. "DRAWING WITH FAT EDGES." International Journal of Foundations of Computer Science 17, no. 05 (2006): 1143–63. http://dx.doi.org/10.1142/s0129054106004315.

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Traditionally, graph drawing algorithms represent vertices as circles and edges as curves connecting the vertices. We introduce the problem of drawing with "fat" edges, i.e., with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional information. We present a model for drawing with fat edges and a corresponding efficient polynomial time algorithm that uses the model. We first focus on a restricted class of graphs that occur in VLSI wire routing and then show how to extend the algorithm to general planar

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15

McCreary, C. L., R. O. Chapman, and F. S. Shieh. "Using graph parsing for automatic graph drawing." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 28, no. 5 (1998): 545–61. http://dx.doi.org/10.1109/3468.709599.

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16

Brückner, Guido, Nadine Krisam, and Tamara Mchedlidze. "Level-Planar Drawings with Few Slopes." Algorithmica 84, no. 1 (2021): 176–96. http://dx.doi.org/10.1007/s00453-021-00884-x.

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AbstractWe introduce and study level-planar straight-line drawings with a fixed number $$\lambda $$ λ of slopes. For proper level graphs (all edges connect vertices of adjacent levels), we give an $$O(n \log ^2 n / \log \log n)$$ O ( n log 2 n / log log n ) -time algorithm that either finds such a drawing or determines that no such drawing exists. Moreover, we consider the partial drawing extension problem, where we seek to extend an immutable drawing of a subgraph to a drawing of the whole graph, and the simultaneous drawing problem, which asks about the existence of drawings of two graphs wh

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17

Friedrich, Carsten, and Peter Eades. "Graph Drawing in Motion." Journal of Graph Algorithms and Applications 6, no. 3 (2002): 353–70. http://dx.doi.org/10.7155/jgaa.00057.

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18

Tantau, Till. "Graph Drawing in TikZ." Journal of Graph Algorithms and Applications 17, no. 4 (2013): 495–513. http://dx.doi.org/10.7155/jgaa.00301.

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19

Frishman, Y., and A. Tal. "Online Dynamic Graph Drawing." IEEE Transactions on Visualization and Computer Graphics 14, no. 4 (2008): 727–40. http://dx.doi.org/10.1109/tvcg.2008.11.

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20

Cohen, Robert F. "Dynamic graph drawing (abstract)." ACM SIGACT News 24, no. 1 (1993): 60. http://dx.doi.org/10.1145/152992.153005.

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21

Papakostas, A., and I. G. Tollis. "Interactive orthogonal graph drawing." IEEE Transactions on Computers 47, no. 11 (1998): 1297–309. http://dx.doi.org/10.1109/12.736444.

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22

Cohen, R. F., P. Eades, Tao Lin, and F. Ruskey. "Three-dimensional graph drawing." Algorithmica 17, no. 2 (1997): 199–208. http://dx.doi.org/10.1007/bf02522826.

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23

Jing-wei, Huang, and Wei Wen-fang. "Evolutionary graph drawing algorithms." Wuhan University Journal of Natural Sciences 8, no. 1 (2003): 212–16. http://dx.doi.org/10.1007/bf02899481.

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24

Koch, Sebastian. "About Supergraphs. Part II." Formalized Mathematics 26, no. 2 (2018): 125–40. http://dx.doi.org/10.2478/forma-2018-0010.

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Summary In the previous article [5] supergraphs and several specializations to formalize the process of drawing graphs were introduced. In this paper another such operation is formalized in Mizar [1], [2]: drawing a vertex and then immediately drawing edges connecting this vertex with a subset of the other vertices of the graph. In case the new vertex is joined with all vertices of a given graph G, this is known as the join of G and the trivial loopless graph K1. While the join of two graphs is known and found in standard literature (like [9], [4], [8] and [3]), the operation discribed in this

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25

Czap, Július, and Peter Sugerek. "Drawing graph joins in the plane with restrictions on crossings." Filomat 31, no. 2 (2017): 363–70. http://dx.doi.org/10.2298/fil1702363c.

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A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. In 2014, Zhang showed that the set of all 1-planar graphs can be decomposed into three classes C0,C1 and C2 with respect to the types of crossings. He proved that every n-vertex 1-planar graph of class C1 has a C1-drawing with at most 3/5n-6/5 crossings. Consequently, every n-vertex 1-planar graph of class C1 has at most 18/5n ? 36/5 edges. In this paper we prove a stronger result. We show that every C1-drawing of a 1-planar graph has at most 3/5n ? 6/5 crossings. Next we

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26

Alegría, Carlos, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, Fabrizio Grosso, and Maurizio Patrignani. "Unit-length Rectangular Drawings of Graphs." Journal of Graph Algorithms and Applications 28, no. 1 (2024): 403–37. http://dx.doi.org/10.7155/jgaa.v28i1.2996.

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A rectangular drawing of a planar graph $G$ is a planar drawing of $G$ in which vertices are mapped to grid points, edges are mapped to horizontal and vertical straight-line segments, and faces are drawn as rectangles. Sometimes this latter constraint is relaxed for the outer face. In this paper, we study rectangular drawings in which the edges have unit length. We show a complexity dichotomy for the problem of deciding the existence of a unit-length rectangular drawing, depending on whether the outer face must also be drawn as a rectangle or not. Specifically, we prove that the problem is NP-

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27

MIURA, KAZUYUKI, SHIN-ICHI NAKANO, and TAKAO NISHIZEKI. "CONVEX GRID DRAWINGS OF FOUR-CONNECTED PLANE GRAPHS." International Journal of Foundations of Computer Science 17, no. 05 (2006): 1031–60. http://dx.doi.org/10.1142/s012905410600425x.

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A convex grid drawing of a plane graph G is a drawing of G on the plane such that all vertices of G are put on grid points, all edges are drawn as straight-line segments without any edge-intersection, and every face boundary is a convex polygon. In this paper we give a linear-time algorithm for finding a convex grid drawing of every 4-connected plane graph G with four or more vertices on the outer face. The size of the drawing satisfies W + H ≤ n - 1, where n is the number of vertices of G, W is the width and H is the height of the grid drawing. Thus the area W · H is at most ⌈(n - 1)/2⌉ · ⌊(n

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28

Akhsani, Lukmanul, and Erlin Nurhayati. "The Error in Drawing Graphic of Quadratic Function in PBL Model by Using True or False Strategy with GeoGebra-Assisted." AlphaMath : Journal of Mathematics Education 6, no. 2 (2020): 135. http://dx.doi.org/10.30595/alphamath.v6i2.8059.

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Quadratic function is one of the important topic in mathematics. The purpose of this study is to describe the mistakes made by students when drawing a quadratic function graph. In this research, the focus of the problem is what type of mistakes made by students in drawing a graph of quadratic functions. The form of error here referred to an error in doing the exercise of drawing quadratic function graph in learning with the PBL model using a true or false strategy assisted by GeoGebra application. The conclusion of this research states that the error in drawing quadratic function graph is domi

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Qu, Jianhua, Xiyu Liu, Minghe Sun, and Feng Qi. "GPU-Based Parallel Particle Swarm Optimization Methods for Graph Drawing." Discrete Dynamics in Nature and Society 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2013673.

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Particle Swarm Optimization (PSO) is a population-based stochastic search technique for solving optimization problems, which has been proven to be effective in a wide range of applications. However, the computational efficiency on large-scale problems is still unsatisfactory. A graph drawing is a pictorial representation of the vertices and edges of a graph. Two PSO heuristic procedures, one serial and the other parallel, are developed for undirected graph drawing. Each particle corresponds to a different layout of the graph. The particle fitness is defined based on the concept of the energy i

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30

Sharma, Jitendra, and Shubhra Saxena. "Enhanced JGraphEd Drawing Framework for Graph Drawing Application." International Journal of Computer Applications 81, no. 4 (2013): 11–16. http://dx.doi.org/10.5120/13999-2037.

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31

Wang, Eric Ke, and Futai Zou. "A New Graph Drawing Scheme for Social Network." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/930314.

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With the development of social networks, people have started to use social network tools to record their life and work more and more frequently. How to analyze social networks to explore potential characteristics and trend of social events has been a hot research topic. In order to analyze it effectively, a kind of techniques called information visualization is employed to extract the potential information from the large scale of social network data and present the information briefly as visualized graphs. In the process of information visualization, graph drawing is a crucial part. In this pa

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32

Shiono, Yasunori, Tadaaki Kirishima, Yoshinori Ueda, and Kensei Tsuchida. "Drawing Algorithm for Fuzzy Graphs Using the Partition Tree." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 5 (2012): 641–52. http://dx.doi.org/10.20965/jaciii.2012.p0641.

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Fuzzy graphs have been used frequently and effectively as a method for sociogram analysis. A fuzzy graph has the fundamental characteristic of being able to express a variety of relationships between nodes. The drawing of fuzzy graphs has been studied in computer-aided analysis systems with human interfaces and methods using genetic algorithms. However, computer-aided analysis systems with human interfaces do not provide for automatic drawing, while methods using genetic algorithms have the defect of requiring too much execution time for finding a locally optimum solution. To overcome these de

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Calamoneri, Tiziana, Simone Jannelli, and Rossella Petreschi. "Experimental Comparison of Graph Drawing Algorithms for Cubic Graphs." Journal of Graph Algorithms and Applications 3, no. 2 (1999): 1–23. http://dx.doi.org/10.7155/jgaa.00013.

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34

FRATI, FABRIZIO. "ON MINIMUM AREA PLANAR UPWARD DRAWINGS OF DIRECTED TREES AND OTHER FAMILIES OF DIRECTED ACYCLIC GRAPHS." International Journal of Computational Geometry & Applications 18, no. 03 (2008): 251–71. http://dx.doi.org/10.1142/s021819590800260x.

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It has been shown that there exist planar digraphs that require exponential area in every upward straight-line planar drawing. On the other hand, upward poly-line planar drawings of planar graphs can be realized in Θ(n2) area. In this paper we consider families of DAGs that naturally arise in practice, like DAGs whose underlying graph is a tree (directed trees), is a bipartite graph (directed bipartite graphs), or is an outerplanar graph (directed outerplanar graphs). Concerning directed trees, we show that optimal Θ(n log n) area upward straight-line/poly-line planar drawings can be construct

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35

Tollis, Ioannis G. "Graph drawing and information visualization." ACM Computing Surveys 28, no. 4es (1996): 19. http://dx.doi.org/10.1145/242224.242247.

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36

Tamassia, Roberto, and Ioannis G. Tollis. "Report on graph drawing '94." ACM SIGACT News 26, no. 1 (1995): 87–91. http://dx.doi.org/10.1145/203610.203615.

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37

Stone, Roger, Firat Batmaz, and Chris Hinde. "Drawing and Marking Graph Diagrams." Innovation in Teaching and Learning in Information and Computer Sciences 8, no. 2 (2009): 45–52. http://dx.doi.org/10.11120/ital.2009.08020045.

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38

Pisanski, Tomaž, and John Shawe-Taylor. "Characterizing Graph Drawing with Eigenvectors‡." Journal of Chemical Information and Computer Sciences 40, no. 3 (2000): 567–71. http://dx.doi.org/10.1021/ci9900938.

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39

Michailidis, George, and Jan de Leeuw. "Data Visualization through Graph Drawing." Computational Statistics 16, no. 3 (2001): 435–50. http://dx.doi.org/10.1007/s001800100077.

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40

Purchase, HELEN C. "Metrics for Graph Drawing Aesthetics." Journal of Visual Languages & Computing 13, no. 5 (2002): 501–16. http://dx.doi.org/10.1006/jvlc.2002.0232.

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TAMASSIA, ROBERTO, IOANNIS G. TOLLIS, and JEFFREY SCOTT VITTER. "A Parallel Algorithm for Planar Orthogonal Grid Drawings." Parallel Processing Letters 10, no. 01 (2000): 141–50. http://dx.doi.org/10.1142/s0129626400000147.

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In this paper we consider the problem of constructing planar orthogonal grid drawings (or more simply, layouts) of graphs, with the goal of minimizing the number of bends along the edges. We present optimal parallel algorithms that construct graph layouts with O(n) maximum edge length, O(n2) area, and at most 2n+4 bends (for biconnected graphs) and 2.4n+2 bends (for simply connected graphs). All three of these quality measures for the layouts are optimal in the worst case for biconnected graphs. The algorithm runs on a CREW PRAM in O( log n) time with n/ log n processors, thus achieving optima

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42

Shiono, Yasunori, Toshihiro Yoshizumi, and Kensei Tsuchida. "Improvement of Fuzzy Graph Drawing Using Partition Tree." Journal of Advanced Computational Intelligence and Intelligent Informatics 26, no. 1 (2022): 17–22. http://dx.doi.org/10.20965/jaciii.2022.p0017.

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Obtaining useful information from ambiguous information is a necessity in various fields. Ambiguous information can be handled quantitatively by using fuzzy theory, and representing it in an easy-to-understand manner is critical. One solution is to visualize an ambiguous relationship by using fuzzy graph representation, which has the essential characteristic of expressing variable relationships in between its nodes. We previously proposed an algorithm to draw intelligible and comprehensive fuzzy graphs. This study describes an improved drawing method for that graph drawing algorithm. As a resu

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43

Sokas, Algirdas. "Intelligent Agent Find its Way in the Drawing." Solid State Phenomena 165 (June 2010): 425–30. http://dx.doi.org/10.4028/www.scientific.net/ssp.165.425.

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This article analyzes intelligent agent in the changing drawing. The objective is to find the shortest way between two points in the flat space with prominent polygon fences. This is an idealized task that a robot (agent) has to solve seeking to find its way in the environment (drawing). The creation tasks of intelligent agent are solved with agent unified modeling language. Graphical system can analyze drawing, forming graph, calculate graph matrices, extract route and prepare programs form with information. It discerns objects-classes: agent, graph, route, which have some properties and meth

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Hua, Jie, Mao Lin Huang, Weidong Huang, and Chenglin Zhao. "Applying Graph Centrality Metrics in Visual Analytics of Scientific Standard Datasets." Symmetry 11, no. 1 (2019): 30. http://dx.doi.org/10.3390/sym11010030.

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Graphs are often used to model data with a relational structure and graphs are usually visualised into node-link diagrams for a better understanding of the underlying data. Node-link diagrams represent not only data entries in a graph, but also the relations among the data entries. Further, many graph drawing algorithms and graph centrality metrics have been successfully applied in visual analytics of various graph datasets, yet little attention has been paid to analytics of scientific standard data. This study attempts to adopt graph drawing methods (force-directed algorithms) to visualise sc

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ZHANG, Wei, Rui-bi ZENG, and Ming-xiao HU. "Weight-length consistent graph drawing algorithm for weighted undirected graphs." Journal of Computer Applications 32, no. 4 (2013): 1116–18. http://dx.doi.org/10.3724/sp.j.1087.2012.01116.

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46

QUAN, Wu. "Fast Convergence Layout Algorithm for Drawing Graphs in Marching-Graph." Journal of Software 19, no. 8 (2008): 1920–32. http://dx.doi.org/10.3724/sp.j.1001.2008.01920.

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47

Raksha, M. R., P. Hithavarshini, Charles Dominic, and N. K. Sudev. "Injective coloring of complementary prism and generalized complementary prism graphs." Discrete Mathematics, Algorithms and Applications 12, no. 02 (2020): 2050026. http://dx.doi.org/10.1142/s1793830920500263.

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The complementary prism [Formula: see text] of a graph [Formula: see text] is the graph obtained by drawing edges between the corresponding vertices of a graph [Formula: see text] and its complement [Formula: see text]. In this paper, we generalize the concept of complementary prisms of graphs and determine the injective chromatic number of generalized complementary prisms of graphs. We prove that for any simple graph [Formula: see text] of order [Formula: see text], [Formula: see text] and if [Formula: see text] is a graph with a universal vertex, then [Formula: see text].

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48

Merrell, Paul. "Example-Based Procedural Modeling Using Graph Grammars." ACM Transactions on Graphics 42, no. 4 (2023): 1–16. http://dx.doi.org/10.1145/3592119.

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We present a method for automatically generating polygonal shapes from an example using a graph grammar. Most procedural modeling techniques use grammars with manually created rules, but our method can create them automatically from an example. Our graph grammars generate graphs that are locally similar to a given example. We disassemble the input into small pieces called primitives and then reassemble the primitives into new graphs. We organize all possible locally similar graphs into a hierarchy and find matching graphs within the hierarchy. These matches are used to create a graph grammar t

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49

Nešetril, Jaroslav. "Art of Graph Drawing and Art." Journal of Graph Algorithms and Applications 6, no. 1 (2002): 131–47. http://dx.doi.org/10.7155/jgaa.00047.

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50

Gajer, Pawel, and Stephen G. Kobourov. "GRIP: Graph Drawing with Intelligent Placement." Journal of Graph Algorithms and Applications 6, no. 3 (2002): 203–24. http://dx.doi.org/10.7155/jgaa.00052.

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