R
Rishtaara
Discrete Mathematics
Lesson 5 of 11Article18 min

Graph Theory Basics

A graph G=(V,E) models networks, dependencies, and maps. Degree, paths, cycles, and connectivity are the everyday vocabulary.

Vertices and edges

A graph G=(V,E) models networks, dependencies, and maps. Degree, paths, cycles, and connectivity are the everyday vocabulary.

  • Bipartite: colourable with 2 colours; no odd cycles.
  • Euler path: exactly 0 or 2 odd-degree vertices.
  • Hamilton path: visits each vertex once — NP-hard to decide in general.
  • Directed graphs: edges have orientation; DAGs model dependencies.