K m,n (complete bipartite graph)
The notation K m,n represents a complete bipartite graph, also known as a bipartite complete graph
The notation K m,n represents a complete bipartite graph, also known as a bipartite complete graph.
A bipartite graph is a type of graph where the vertices can be divided into two disjoint sets such that no edges exist between vertices within the same set. In other words, there are no edges connecting any two vertices within the same group.
In the case of a complete bipartite graph, it has two sets of vertices, let’s say set A and set B. The number of vertices in set A is denoted by m, and the number of vertices in set B is denoted by n. Each vertex in set A is connected to every vertex in set B, resulting in a total of m * n edges. There are no edges between vertices within set A or set B.
The complete bipartite graph K m,n can be visualized as two distinct sets of vertices, where every vertex from set A is connected to every vertex in set B. This graph can be represented as a set of points and lines connecting these points, where the points belong to either set A or set B.
It is worth noting that the complete bipartite graph K m,n can be symmetric, meaning that if you interchange the labels of set A and set B, you obtain the same graph. However, it is not necessary for m to equal n for a complete bipartite graph; the two sets can have different numbers of vertices.
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