Area bounds of hierarchical graphs straightline grid drawing

Hierarchical graphs propose an important class of graphs for modeling many real applications in software and information visualization. Actually, the ability to construct area-efficient drawings is essential in many practical visualization applications. In this paper, we consider the problem of the drawing area needed to draw a hierarchical graph in the grid. We applied practical analysis in order to find the relation between the grid drawing area of a hierarchical graph and its number of vertices. We introduce two new mathematical formulations for the minimum and maximum grid drawing areas hierarchical graph.