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Print Thing Tag# Summary

Discrete mathematics: K4 - Connected graph with four vertices.

# Print Settings

**Printer: **

Alunar M508

**Rafts: **

No

**Supports: **

Yes

**Resolution: **

0.2

**Infill: **

100

# Standards

# Overview and Background

**Connected Graphs**

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

= 6.

# Lesson Plan and Activity

**Introduction to Connected Graphs**

Introduce vertices and edges, graphs.

Introduce vertex degree.

Introduce graph connectivity.

K4.

Add vertices and edges to create K5, K6, ... ,Kn

Define connected graph properties

Define how to determine if a graph is connected

# Materials Needed

PLA or ABS filament, 3D printer, 3D model of K4.

Then, you can use a whiteboard to expand on graph connectedness with your class.