Vertex count refers to the total number of vertices in a geometric shape or graph. In geometry, a vertex is a point where two or more edges meet, such as the corners of a polygon. For example, a triangle has three vertices, while a cube has eight. In graph theory, vertex count is crucial for analyzing the structure of a graph, which consists of vertices connected by edges. The vertex count helps determine properties like connectivity and the overall complexity of the graph. Understanding vertex count is essential in fields like computer science, mathematics, and network analysis.