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Discrete math
Please break this down so that a child can understand. Please
explain how to find the chromatic polynomial for a graph.
4. Find the chromatic polynomial of the graph in Figure 2 (below): d e с f b а Figure 3, G Solution: Let's use the deletion-contraction theorem. We start with edge ef (Figure 4 and 3

Figure 5): Figure 4, G1 Figure 5, G2 So, we have XG(t) = XG(t) – XG(t). We computed XG (t) in class: XG (t) = t(t - 1)(t - 2)(t2 – 3t+ 3). For the graph G2, we have two pendant edges (an edge incident to a vertex with degree 1). What happens if we have a connected graph T that is obtained from a graph S by adding an edge that makes it pendant? Then the same theorem applied to that edge gives xr(t) = Xsu{u}(t) – Xs(t) = xs(t)t – xs(t) = xs(t)(t – 1). So, the effect of adding a pendant edge to a graph in the chromatic polynomial is to multiply', by (t - 1). Since the four cycle (we did in class) has chromatic polynomial equal to t(t – 1)(t2 - 3t+3), we obtain that XG (t) = t(t – 1)(t2 – 3t + 3). = As a result we get XG(t) = XG(t) - XG;(t) =t(t - 1)(t- 3t+3)(t2 - 2t +1-t+2) = xo(t) =t(t - 1)(– 3t+3)2 =