A complete graph is a type of graph in which every pair of distinct vertices is connected by a unique edge. In mathematical terms, a complete graph with n vertices is denoted as K_n . For example, K_3 has three vertices, and each vertex is connected to the other two, resulting in three edges. Complete graphs are important in graph theory and have applications in various fields, including computer science and network design. The number of edges in a complete graph can be calculated using the formula \fracn(n-1)2 , where n is the number of vertices.