Graph theory is used in computer science for routing algorithms, data structures, and database management.

In network analysis, a graph is represented by nodes (vertices) and edges (arcs).

Hamiltonian cycle is used in scheduling problems to find a tour that visits all nodes exactly once and returns to the starting node.

In social network analysis, a graph can represent individuals and their relationships, groups and their interactions, or events and their connections.

Planar graph is used in circuit analysis to represent circuits that can be drawn on a plane without any crossings.

Chromatic number is used in map coloring problems to determine the minimum number of colors needed to color a map so that no two adjacent regions have the same color.

Dijkstra's algorithm is used in routing algorithms to find the shortest path between two nodes in a graph.

Critical path method, PERT chart, and Gantt chart are all graph theory concepts used in scheduling problems.

Flow network, max-flow min-cut theorem, and shortest path are all graph theory concepts used in network analysis.

Planar graph is used in graph drawing to represent graphs that can be drawn on a plane without any crossings.

Hypergraph, clique, and independent set are all graph theory concepts used in VLSI design.

Linear programming, integer programming, and dynamic programming are all graph theory concepts used in operations research.

Game tree, Nash equilibrium, and prisoner's dilemma are all graph theory concepts used in game theory.

Phylogenetic tree, food web, and protein-protein interaction network are all graph theory concepts used in biology.

Input-output model, social network, and game theory are all graph theory concepts used in economics.