Discrete mathematics: K4 - Connected graph with four vertices.
Overview and Background
A connected graph is a graph in which each vertex is a path connecting any two vertices. K4 is a connected graph with 4 vertices.
In general, a connected graph has n vertices each of degree n-1. Fir example in K4 there are 4 vertices each of degree 3.
The degree of a vertex is the number of edges coming in to or out of a vertex. Then by this definition, a connected graph must have n(n-1) / 2 edges. With K4, there are 4 vertices and 6 edges. To compute the number of edges:
4(4-1) / 2
= 4(3) / 2
= 12 / 2
Lesson Plan and Activity
Introduction to Connected Graphs
Introduce vertices and edges, graphs.
Introduce vertex degree.
Introduce graph connectivity.
Add vertices and edges to create K5, K6, ... ,Kn
Define connected graph properties
Define how to determine if a graph is connected
PLA or ABS filament, 3D printer, 3D model of K4.
Then, you can use a whiteboard to expand on graph connectedness with your class.