🎓 Deeper Dive — Adults

A graph G = (V, E) is a set of vertices V and edges E ⊆ V × V.

Degree of v = number of edges incident to v. Handshake lemma: Σ deg(v) = 2|E|.

Path: sequence of edges. Cycle: closed path. Tree: connected acyclic graph (n vertices → n−1 edges). Eulerian: traverses every edge once (possible iff all vertices have even degree).

Algorithms: BFS, DFS, Dijkstra (shortest path), Kruskal/Prim (MST), Floyd-Warshall (all-pairs).