Lesson 094
Graph Types
Simple · Tree · Complete\nBipartite · Planar · DAG
1:00The seven graph families — simple, multigraph, tree, complete, bipartite, planar, and DAG — and the structural properties that determine which algorithms work on each.
By the end, you can
- Distinguish simple graphs from multigraphs and state what each permits or forbids.
- Classify a graph as a tree, forest, complete, bipartite, planar, or DAG from its properties.
- Apply the edge-count formulas: n − 1 for trees, n(n−1)/2 for complete graphs, V − k for forests.
- Explain why a triangle cannot be bipartite, using the odd-cycle theorem.
- State Euler's formula for planar graphs and derive the E ≤ 3V − 6 sparsity bound.
- Explain why a directed graph has a topological order if and only if it is a DAG.
- Identify real-world systems (build tools, schedulers, road networks, matching problems) by their graph family.
Up next in Trees, Hashing & Graphs
