For edge colourable the maximum no. of edges co- incides at S which are 3+4 = 7 because each vetex of k3,4 is connected to S according to Question
so atleast 7 distinct colours are required to edge colour K3,4
if it is asked for vertex coloring then
For Vertex coloring no. of colours required is 2 for each set (3,4) and 1 for adjacent vertex S
So, K3,4 with S as adjacent is 3 colourable