11.5: Summary
- Page ID
- 60131
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- Graphs are defined by sets, not by diagrams
- Deleting a vertex or edge
- How to use proofs by induction on graphs
- Euler’s handshaking lemma
- Graph invariants, distinguishing between graphs
- Labeled and unlabeled graphs
- Important Definitions:
- Graph, Vertex, Edge
- Loop, Multiple Edge, Multigraph, Simple Graph
- Endvertex, incident, adjacent, neighbour
- Degree, Valency, Isolated Vertex
- Subgraph
- Complete Graph
- Isomorphic graphs, Isomorphism between graphs
- Notation:
- \(u ∼ v\)
- \(uv\)
- \(\text{val}(v), \text{deg}(v), d(v), d_G(v)\)
- \(G \setminus \{v\}, G \setminus \{e\}\)
- \(K_n\)
- \(G_1 \cong G_2\)