Types of Graphs
Simple, directed, weighted, complete, bipartite.
Key idea
Simple, directed, weighted, complete, bipartite.
In depth
Common types: complete (Kₙ, every pair adjacent), cycle (Cₙ), path (Pₙ), tree, bipartite, regular (all degrees equal), and directed graphs. Naming types helps recognise known results.
Worked example
Kₙ has n(n − 1)/2 edges: K₅ has 10.
Real-world uses
- Choosing the right model for one-way streets (directed), road distances (weighted) or job matching (bipartite)
Common mistake
Mixing up complete graphs with complete bipartite graphs.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Types of Graphs?
Simple, directed, weighted, complete, bipartite. It is a topic at the advanced level in Discrete Math & Number Theory.
Where is Types of Graphs used in real life?
Real-world examples: Choosing the right model for one-way streets (directed), road distances (weighted) or job matching (bipartite).
What should I learn before Types of Graphs?
Make sure you are comfortable with Degree and Handshake Lemma, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Types of Graphs?
Mixing up complete graphs with complete bipartite graphs.
How can I practise Types of Graphs?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Types of Graphs?
Move on to Paths, Cycles and Connectivity next.
Related advanced topics in Discrete Math & Number Theory
- Tautologies and Contradictions – Always true or always false statements.
- Logical Equivalence – Statements with identical truth tables.
- De Morgan’s Laws – Negation swaps AND and OR.
- Converse and Contrapositive – A conditional equals its contrapositive.
- Quantifiers – “For all” and “there exists”.
- Negating Quantified Statements – Flip the quantifier and negate the predicate.