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 represents a triangle, where each vertex is connected to every other vertex. Complete graphs are significant in graph theory because they serve as a fundamental structure for various problems and algorithms. 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. This property makes complete graphs useful in fields like network design and combinatorial optimization.