Graphs and Combinatorics

Graphs and combinatorics are branches of mathematics that deal with understanding relationships and counting possibilities. Graphs use points (called vertices) connected by lines (edges) to model networks like social connections, transportation systems, or data structures. Combinatorics focuses on counting, arranging, and selecting objects—helping determine how many ways things can be organized or combined. Together, they provide tools for analyzing complex systems, optimizing routes, solving puzzles, and making decisions based on possible arrangements or connections, applicable in numerous fields from computer science to logistics and beyond.