【實用教育app】Graph Theory|最夯免費app-gigacircle

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.