1. The problem is to define graphs using concepts from discrete mathematics, specifically elements of graph theory. 2. A graph $G$ is defined as an ordered pair $G = (V, E)$ where: - $V$ is a non-empty set of vertices (or nodes). - $E$ is a set of edges, which are unordered pairs of vertices if the graph is undirected, or ordered pairs if directed. 3. Important rules and concepts: - Vertices represent entities or points. - Edges represent connections or relationships between vertices. - A graph can be simple (no loops or multiple edges) or multigraph (may have multiple edges). - Directed graphs (digraphs) have edges with direction. - Degree of a vertex is the number of edges incident to it. 4. Example: If $V = \{1, 2, 3\}$ and $E = \{\{1, 2\}, \{2, 3\}\}$, then $G$ is a simple undirected graph with three vertices and two edges. 5. In summary, graph theory studies these structures to analyze relationships and connections in discrete systems.