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The number of edges in a complete bipartite graph ๐พ๐‘š,๐‘›K m,nโ€‹ is:A. ๐‘š+๐‘›m+nB. ๐‘š๐‘›mnC. ๐‘š+๐‘›โˆ’1m+nโˆ’1D. ๐‘š๐‘›โˆ’1mnโˆ’1

Question

The number of edges in a complete bipartite graph ๐พ๐‘š,๐‘›K m,nโ€‹ is:A. ๐‘š+๐‘›m+nB. ๐‘š๐‘›mnC. ๐‘š+๐‘›โˆ’1m+nโˆ’1D. ๐‘š๐‘›โˆ’1mnโˆ’1

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Solution

A complete bipartite graph ๐พ๐‘š,๐‘› is a graph whose vertices can be divided into two disjoint sets of m and n vertices such that every vertex in the first set is connected to every vertex in the second set.

The number of edges in a complete bipartite graph ๐พ๐‘š,๐‘› is given by the product of the number of vertices in each set. This is because each vertex in one set is connected to every vertex in the other set.

So, the number of edges in a complete bipartite graph ๐พ๐‘š,๐‘› is ๐‘š๐‘› (option B).

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