Graph Theory
Explore graph structures; paths, coloring and planarity; networks and spectral viewpoints. Concepts and connections are available independently of video coverage.
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Planar graphs
A planar graph can be drawn without edge crossings except at shared endpoints.
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Euler and Hamilton paths
Euler paths traverse each edge once; Hamilton paths visit each vertex once.
Graph coloring
Proper vertex coloring assigns different colors to adjacent vertices.
Graph Laplacian
For a simple undirected graph, degree matrix minus adjacency matrix encodes connectivity and diffusion.
Graph connectivity
Paths determine connected components; vertex and edge connectivity quantify robustness to removal.
Vertex degrees
Degree counts incident edge ends; directed graphs distinguish incoming and outgoing degrees.
Knowledge connections
- Graph coloring · Related · Map context
- Euler and Hamilton paths · Related · Map context