Abstract: Hierarchical planar graph embedding (sometimes called level planar graphs) is widely recognized as a very important task in diverse fields of research and development. Given a proper hierarchical planar graph, we want to find a geometric position of every vertex (layout) in a straight-line grid drawing without any edge-intersection. An additional objective is to minimize the area of the rectangular grid in which G is drawn with more aesthetic embedding. In this paper we propose several ideas to find an embedding of G in a rectangular grid with area, ( -1) × (k-1), where is the number of vertices in the longest level and k is the number of levels in G.)

Mohamed A. El Sayed, Ahmed A. A. Radwan and Nahla F. Omran , “Study of Proper Hierarchical Graphs on a Grid” International Journal of Advanced Computer Science and Applications(IJACSA), 3(12), 2012. http://dx.doi.org/10.14569/IJACSA.2012.031216

@article{Sayed2012,
title = {Study of Proper Hierarchical Graphs on a Grid},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2012.031216},
url = {http://dx.doi.org/10.14569/IJACSA.2012.031216},
year = {2012},
publisher = {The Science and Information Organization},
volume = {3},
number = {12},
author = {Mohamed A. El Sayed and Ahmed A. A. Radwan and Nahla F. Omran }
}