complete graph
all vertices are adjacent to each other
A complete graph is a mathematical concept that refers to a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. In other words, a complete graph is one in which there is a direct edge between every pair of vertices in the graph.
A complete graph with n vertices is often represented by the symbol Kn, where n represents the number of vertices. For example, a complete graph with 5 vertices would be represented as K5.
Complete graphs are commonly used in graph theory and can be used to model structures such as social networks or transportation networks, where every entity (represented by a vertex) is connected to every other entity.
There are a number of interesting properties associated with complete graphs. One of the most notable is that the total number of edges in a complete graph with n vertices is given by the formula n(n-1)/2. So, for example, a complete graph with 5 vertices would have 10 edges.
Complete graphs are also useful in certain applications of graph theory, since they represent extreme cases where every vertex is connected to every other vertex.
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