In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
What is the best open source program for drawing the planar graph with support of input nodes size and fixed drawing boundary region
I'd suggest use build your own using boost-graph libraries. A good information can be found on Donald knuth home page. There are some softwares which I have not used very much. Graphthing is one of those. I do not think it'll meet your requirement. If you are a research guy, then I personally recommend not to be inclined towards visualization of graphs.
I have a few pointers for graph visualization methods:
Prefuse - original version is in Java and the newer stuff is flash.
Networkx with matplotlib - all in python
Ubigraph - for animated 3D visualization
I've found this one useful for all kinds of 2D work..
http://www.yworks.com/en/products_yed_about.html
It's java based so you should be able to run it anywhere you have a suitable jvm.