Thursday 28th of March 2024
 

New Approach for Drawings of 3-Planar Graphs


Mohamed A. El-Sayed, Shimaa E. Waheed, Amal Ali M. Mady and S. Abdel-Khalek

The field of graph drawing is concerned with finding algorithms to draw graph in an aesthetically pleasant way, based upon a certain number of aesthetic criteria that define what a good drawing, (synonyms: diagrams, pictures, layouts), of a graph should be. This problem can be found in many such as in the computer networks, data networks, class interrelationship diagrams in object oriented databases and object oriented programs, visual programming interfaces, database design systems, software engineering, etc. Given a plane graph G, we wish to find a drawing of G in the plane such that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints without any edge-intersection. Such drawings are called planar straight-line drawings of G. An additional objective is to minimize the area of the rectangular grid in which G is drawn. In this paper we introduce a new algorithms that finds an embedding of 3-planar graph in linear time O(n).

Keywords: 3- Planar Graph; Graph Drawing; drawing on grid.

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ABOUT THE AUTHORS

Mohamed A. El-Sayed
Department of Math, Faculty of Science, Fayoum University, Egypt Department of CS, Computer and IT College, Taif University, KSA;

Shimaa E. Waheed
Department of Math, Faculty of Science, Taif University, KSA; 3 Department of Math, Faculty of Science, Benha University, Egypt;

Amal Ali M. Mady
Department of Math, Faculty of Science, Taif University, KSA;

S. Abdel-Khalek
Department of Math, Faculty of Science, Taif University, KSA;


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