(a) Let Icirc raquo Z If we have Icirc raquo different colors available, in how many ways can we color the vertices of the graph shown in Fig 8 14(a) so that no adjacent vertices share the same color This result in Icirc raquo is called the chromatic polynomial of the graph, and the smallest value of Icirc raquo for which the value of this polynomial is positive is called the chromatic number of the graph What is the chromatic number of this graph (We shall pursue this idea further in Chapter 11 ) (b) If there are six colors available, in how many ways can the rooms Ri, 1 curren i curren 5, shown in Fig 8 14(b) be painted so that rooms with a common doorway, Dj, 1 curren j curren 5, are painted with different colors R1 D3 Rs b) Figure 8 14

Question

(a) Let  Icirc  raquo  Z   If we have  Icirc  raquo  different colors available, in how many ways can we color the vertices of the graph shown in Fig  8 14(a) so that no adjacent vertices share the same color  This result in  Icirc  raquo  is called the chromatic polynomial of the graph, and the smallest value of  Icirc  raquo  for which the value of this polynomial is positive is called the chromatic number of the graph  What is the chromatic number of this graph  (We shall pursue this idea further in Chapter 11 ) (b) If there are six colors available, in how many ways can the rooms Ri, 1  curren  i  curren  5, shown in Fig  8 14(b) be painted so that rooms with a common doorway, Dj, 1  curren  j  curren  5, are painted with different colors  R1 D3 Rs b) Figure 8 14

SolutionInn · Accepted Answer

a Define conditions c i 1 i 5 as follows c 1 a and b have the same color c 2 b and ...

Question: (a) Let Î» Z+. If we have Î» different colors available, in how many ways can we color the vertices of the graph shown in

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