How many edges has the complement of K10 6 Justify your answ

How many edges has the complement of K_10, 6? Justify your answer.

Solution

In Every complete Bipartite graph K n,m is connected (n,m 1). Here Every node “on the right” has an edge to “every node on the left”, here they are connected by a path of length 1. as well as, every node on the right is connected by a path of length 2 to every other node on the right, going through a node, say node 1, on the left.

Like that , Every node on the left is connected by a path of length 2 to every other node on the left.

Now, cosider our problem The Complement of K 10,6 can be calculated by the Handashake theorem,

There is one edge corresponding to each unordered pair of vertices, so the number is 10 base 6   = 60.

i.e, in Handshake we consider , there are 10 vertices, each having degree 6, so the sum of all degrees is (10*6) means it is 60. By the handshake theorem, this is twice the number of edges, so there are 60/2 = 30 edges.) i.e, 60/2= 30 edges.

Finally,The complete bipartite graphs have an edge between every pair of nodes. It does not have edges between nodes on the same side.