✏️ Practice Exercises

Graph Theory

3 problems · Easy to Hard · Type your working · AI checks your steps

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How to use these exercises

Read the question → work it out step-by-step in the box → click Check My Working to get AI feedback. Use hints if stuck. Reveal the full solution only after you have tried.

01

easy

A tree has 12 vertices. How many edges?

💡 Show hint

For a tree: n − 1.

Your Working

02

medium

Sum of degrees in a graph with 7 edges:

💡 Show hint

Handshake lemma: Σ deg = 2|E|.

Your Working

03

hard

Does a graph with vertex degrees {3, 3, 3, 3, 3} exist?

💡 Show hint

Sum of degrees must be even (handshake lemma).

Your Working

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