Calculate E in the complete bigraph Km n V E for m Element

Calculate |E| in the complete bigraph K_m, n = (V, E) for m Element {1, ..., 5} and n Element{1, ..., 5}.

Solution

Consider the given complete bipartite graph K_m,n where m { 1 , 2, 3, 4, 5 } and n { 1 , 2, 3, 4, 5 }.

Clearly the cardinality of m and n are l m l = 5 and l n l = 5

Then there will be an edge from theeach vertex set of m to each vetex of the set n.

Thus there will be l m l x l n l = 5 x 5 = 25 edges in the graph K_m,n

Thus the number of edges in Km,n is l E l = 25