Problem 2.) Complete Bipartite

(2) The complete bipartite graph has a set of m red vertices and a set of n blue vertices, such that every red vertex is joined to every blue vertex, and vice versa (note: colors are irrelevant – for convenience, only). The first graph on this page is the complete bipartite graph . The Mathematica commands:

G= CompleteGraph[m, n]

GraphPlot[G]

return a planar drawing of the complete bipartite graph

 

 

For this problem I simply plugged in the following code in order to receive the complete bipartite graph of the K(4,5).

CompleteGraph[{4, 5}, PlotLabel -> {K4, 5},
VertexStyle -> {1 -> Blue, 2 -> Blue, 3 -> Blue, 4 -> Blue, 5 -> Red,
6 -> Red, 7 -> Red, 8 -> Red, 9 -> Red},
VertexSize -> Medium, VertexLabels -> “Name”]