Graph Theory app for iPhone and iPad

Networks are seemingly ubiquitous across many disciplines, from neurons and synapses in the brain to webpages and links on the internet. A graph is an abstract object which represents the basic structure of nodes and connections in a network.

A graph is usually drawn as a static diagram of vertices and edges, but one must remember that a given graph can have infinitely many such drawings. This app allows the user to interact directly with graph diagrams in real time and thus gain a deeper appreciation of the underlying abstract objects.

Features:

Graph library consisting of many famous and important graphs: e.g. skeleta of Platonic solids, K(5), K(3,3), Petersen graph, etc.

Smooth user interface for drawing and editing graphs. Triple tap to add a new vertex. To draw edges, double tap on a vertex and drag to other vertices. Press and hold to enter erase mode, and then the above gestures will delete vertices and edges.

Highlight the neighbors of a tapped vertex.

Highlight any edge crossings in the current graph diagram.

Generate a "random" planar graph with at most 200 vertices or a "random" maximal planar graph with at most 100 vertices. It is a fun game to try to untangle these graphs. To make the job easier, we provide a local "energy minimization" algorithm and an option to "trim" or "freeze" irrelevant vertices.

List of the minimum crossing numbers of well-known cubic symmetric graphs. It is quite challenging to move the vertices around for these graphs to achieve the minimum number of crossings.

Supported for iOS 5.1 on iPhone and iPad.