Back to Year 12

Graph Theory Explorer

Build graphs · explore isomorphisms · verify Euler's formula

mode: add-nodes
Click anywhere on the canvas to place a node.
0 Vertices (V)
0 Edges (E)
+
0 Faces (F)
=
? V − E + F

Euler's Formula

For any connected planar graph: V − E + F = 2

Isomorphism tip

Two graphs are isomorphic if one can be redrawn to look like the other. Use Move mode to drag nodes and reshape your graph — the structure stays the same!

Faces & regions

A face is a region bounded by edges — including the outer (infinite) region. In Colour faces mode, click the outer face button in the top-left corner of the canvas to colour it.

How to use

1. Add nodes → 2. Connect them with edges → 3. Move nodes to explore isomorphisms → 4. Colour faces to verify V − E + F = 2.