Mathematics · University
Induction, graphs and discrete reasoning · revision notes
Prove a base case and a step from n to n+1; neither alone suffices.
Key ideas and conditions
Induction
Prove a base case and a step from n to n+1; neither alone suffices.
Graph degrees
In a finite undirected graph, the sum of vertex degrees is twice the number of edges.
Trees
A finite connected acyclic graph with n vertices has n−1 edges.
Proof versus pattern
A pattern in numerical examples suggests a conjecture but does not prove it.
Explain without looking
- Explain why removing a leaf and its edge from a tree leaves a smaller tree.
- Does every connected graph have n−1 edges?
Further reading and review references
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