planar graph drawing - t. nishizeki, m. rahman

[...]... following drawing styles 1.3.1 Planar Drawing A drawing of a graph is p l a n a r if no two edges intersect in the drawing Figure 1.3 depicts a planar drawing and a non -planar drawing of the same graph It is preferable to find a planar drawing of a graph if the graph has such a drawing Unfortunately not all graphs admit planar drawings A graph which admits a planar drawing is called a p l a n a r graph. .. Every plane graph has a box-orthogonal drawing Several results are known for box-orthogonal drawings [BK97, FKK97, PTOO] I Fig 1.6 (a) An orthogonal drawing, (b) a box-orthogonal drawing, (c) a rectangular drawing, and (d) a box-rectangular drawing TEAM LinG - Live, Informative, Non-cost and Genuine ! Planar Graph Drawing 8 1.3.7 Rectangular Drawing A rectangular drawing of a plane graph G is a drawing. .. TEAM LinG - Live, Informative, Non-cost and Genuine ! Planar Graph Drawing 16 this book t o the theories and algorithms for drawing planar graphs Particularly, straight line drawings, convex drawings, rectangular drawings, box-rectangular drawings, orthogonal drawings and octagonal drawings of planar graphs are in the scope of this book Exercise 1 Find a straight line drawing of the plane graph in Fig... the concepts of drawing planar graphs are basic building blocks of the field of graph drawing A drawing of a planar graph looks nice and algorithms for drawing planar graphs can be successfully used for drawing a nonplanar graph by transforming the nonplanar graph into a similar planar graph Furthermore, drawings of planar graphs have practical applications in VLSI floorplanning and routing, architectural... drawing of a plane graph TEAM LinG - Live, Informative, Non-cost and Genuine ! Graph Drawing Fig 1.13 Graphs for Exercise 2 Fig 1.14 Graphs for Exercise 3 Fig 1.15 Graph for Exercise 4 TEAM LinG - Live, Informative, Non-cost and Genuine ! 17 18 Planar Graph Drawing Fig 1.16 Graphs for Exercise 5 Fig 1.17 Graph for Exercise 7 TEAM LinG - Live, Informative, Non-cost and Genuine ! Chapter 2 Graph Theoretic... on 3D drawing, dynamic drawing, proximity drawing, map labeling, etc [KWOl] Different classes of graphs such as planar graphs, hierarchical graphs, clustered graphs, interval graphs, etc are investigated to produce graph drawings having some desired properties Therefore it would be difficult to cover all results of graph drawing in a single book In our opinion, the concepts of drawing planar graphs... rectangular drawing and a box-rectangular drawing 7 Find an orthogonal drawing of the plane graph in Fig 1.17 Count the number of bends in your drawing Is the number minimum for an orthogonal drawing of the plane graph? 8 Find a visibility drawing and a 2-visibility drawing of the plane graph in Fig 1.12 9 Mention some similarities and differences between a box-rectangular drawing and a 2-visibility drawing. .. finding a planar embedding of a planar graph Shih and Hsu [SH99] gave a simple TEAM LinG - Live, Informative, Non-cost and Genuine ! Graph Drawing 5 linear-time algorithm which performs planarity testing and finds a planar embedding of a planar graph simultaneously For the interested reader, algorithms for planarity testing and embeddings are given in Appendix A A planar graph with a fixed planar embedding... drawing Does your drawing take the minimum grid size? Fig 1.12 Graph for Exercise 1 2 Find rectangular drawings of the graphs in Fig 1.13 3 The graphs in Fig 1.14 have no rectangular drawings Explain the reasons 4 Find a box-rectangular drawing of the graph in Fig 1.15 5 The plane graphs in Fig 1.16 have no convex drawing Why? 6 Establish relationship among an orthogonal drawing, a box-orthogonal drawing, ... admits a planar drawing is called a p l a n a r graph b d Fig 1.3 (a) A planar drawing, and (b) a non -planar drawing of the same graph If one wants to find a planar drawing of a given graph, first he/she needs t o test whether the given graph is planar or not If the graph is planar, then he/she needs to find a planar embedding of the graph, which is a data structure representing adjacency lists: in each . most of the important theorems and algorithms that are currently known for planar graph drawing. Furthermore, we have tried to provide constructive proofs for theorems, from which algorithms. On the other hand, We now consider another example. 1 TEAM LinG - Live, Informative, Non-cost and Genuine ! 2 Planar Graph Drawing STATION STATION STATION STATION STATION ’’ J STATION. linear-time algorithm which performs planarity testing and finds a planar embedding of a planar graph simultaneously. For the interested reader, algorithms for planarity testing and embeddings