(a) Consider the graph K2,3 shown in Fig. 11.91, and let Z+ denote the number...

(a) Consider the graph K2,3 shown in Fig. 11.91, and let λ ˆˆ Z+ denote the number of colors available to properly color the vertices of K2,3. (i) How many proper colorings of K2,3 have vertices a, b colored the same? (ii) How many proper colorings of K2,3 have vertices a, b colored with different colors?
(b) What is the chromatic polynomial for K2,3? What is X(K2,3)?
(c) For n ˆˆ Z+, what is the chromatic polynomial for K2, n? What is x (K2, J )?

Transcribed Image Text:

2 Figure 11.9t