1. What is a Graph?
A graph is a mathematical structure consisting of vertices and edges.
Formally, a graph is written as:
\[ G = (V, E) \]
where \( V \) is the set of vertices and \( E \) is the set of edges.
2. Hamiltonian and Eulerian Graphs
A graph is Hamiltonian if it contains a cycle \( v_1 \to v_2 \to \cdots \to v_n \to v_1 \) that visits every vertex exactly once.
A graph is Eulerian if it contains a cycle that uses every edge exactly once.