osting by E Abstract A straight-line grid drawing of a planar graph G of n vertices is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. Finding algorithms for straight-line grid drawings of maximal planar graphs (MPGs) in the minimum area is still an elusive goal. In this paper we explore t...

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every series-parallel graph of maximum degree three is three. We also show that the plan...

In this paper, we give a process to enumerate all maximal planar graphs with minimum degree ve, with a xed number of vertices. These graphs are called MPG5 [6]. We have used the algorithm [3] to generate these graphs. For the MPG5 enumeration we have used the general method due to Brenda McKay in [5]; i.e. by computing the orbits set of automorphism group and canonical forms.

We assume that the reader is familiar with the work [ 1 ] and with the notation and results of the first paper [3 1. Further terminology used in this paper will be defined as it appears. In the first paper the recognition of maximal planar graphs was established. We now prove further that this class of graphs is indeed reconstructible. We first recall that the following result was proved by Fio...

It is shown that in a 4-connected maximal planar graph there is for any four vertices a, b, c and d, a cycle in the graph that contains the four vertices and visits them in the order a, b, c and d.

We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by a point-contact or a side-contact between the corresponding polygons. Specifically, we consider proportional contact representations, where given vertex weights are represented by the areas of the corresponding polygons. Several natural optimization goals for such repr...

In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algo...