In this question we will show that for a given graph, G, the number of distinct k-colourings of G is a polynomial in k. More precisely: For a given graph, G = (V, E), and positive integer, k, define the function: fo = |{0:V + [k] : 0 is a proper colouring}| This function counts the number of distinct k colours of G. (b) Draw a connected graph with 7 vertices and pick and edge then draw the graph you get from performing either of these operations to the graph with that edge (so 3 draw graphs in total) (C) Show that the number of edges after performing either operation G - e or G\e reduces the number of edges by at least 1. In this question we will show that for a given graph, G, the number of distinct k-colourings of G is a polynomial in k. More precisely: For a given graph, G = (V, E), and positive integer, k, define the function: fo = |{0:V + [k] : 0 is a proper colouring}| This function counts the number of distinct k colours of G. (b) Draw a connected graph with 7 vertices and pick and edge then draw the graph you get from performing either of these operations to the graph with that edge (so 3 draw graphs in total) (C) Show that the number of edges after performing either operation G - e or G\e reduces the number of edges by at least 1