It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmovic, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.

This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edge-crossings counting while performing adjacent vertex swaps, and a simple and fast spline routing algorithm.

Enabling the user of a graph drawing system to preserve the mental map between two different layouts of a graph is a major problem. In this paper we present methods that smoothly transform one drawing of a graph into another without any restrictions to the class of graphs or type of layout algorithm. Communicated by M. Kaufmann: submitted February 2001; revised February 2002. Research supported...

This thesis covers three aspects in the field of graph analysis and drawing. Firstly, the depth-first-search–based algorithm for finding triconnected components in general biconnected graphs is presented. This linear-time algorithm was originally published by Hopcroft and Tarjan [17], and corrected by Mutzel and Gutwenger [13]. Since the original paper is hard to understand, the algorithm is pr...

A three-dimensional straight-line grid drawing of a graph, henceforth called a 3D drawing, represents the vertices by distinct grid-points in Z and represents each edge by the line segment between its end vertices, such that no two edges cross. In contrast to the case in the plane, it is folklore that every graph has a 3D drawing. For example, the “moment curve” algorithm places the i th vertex...

We study the problem of the amount of information required to draw a complete or a partial map of a graph with unlabeled nodes and arbitrarily labeled ports. A mobile agent, starting at any node of an unknown connected graph and walking in it, has to accomplish one of the following tasks: draw a complete map of the graph, i.e., find an isomorphic copy of it including port numbering, or draw a p...

Graph drawing addresses the problem of constructing geometric representations of abstract graphs and networks. It is an emerging area of research that combines avors of topological graph theory and computational geometry. The automatic generation of drawings of graphs has important applications in key computer technologies such as software engineering, database design, visual interfaces, and co...

deep drawing of cylindrical shapes with high limiting drawing ratio (ldr) values is relatively difficult. annealing is a further operation, which in turn adds costs and consumes significantly time to the forming process. in the present work, cylindrical cups from brass sheet were made with only limited anneal during few steps, but having ldr of 9 that is about 2 times higher than previous works...

We investigate the distribution, mean value, variance and some limiting properties of an urn model of white and red balls under random multiple drawing (either with or without replacement) when the number of white and red balls added follows a schedule that depends on the number of white balls chosen in each drawing.