1. The vertex method is a technique used in decision mathematics, particularly in graph theory and optimization problems. 2. It involves analyzing the vertices (or nodes) of a graph to find optimal paths, matchings, or other properties. 3. For example, in shortest path problems, the vertex method helps identify the best route by examining connections between vertices. 4. The method often uses algorithms like Dijkstra's or Bellman-Ford, which systematically explore vertices and update distances. 5. Key rules include considering all vertices, updating path costs, and ensuring no negative cycles in the graph. 6. In summary, the vertex method focuses on vertices to solve decision problems efficiently by leveraging graph structures.