For n 3, recall that the wheel graph, Wn, is obtained from a cycle of length
Question:
(a) What relationship is there between x (Cn) and x (Wn)?
(b) Use part (e) of Exercise 15 to show that
P(Wn, λ) = λ(λ - 2)n + (-1 )nλ(λ - 2).
(c) (i) If we have k different colors available, in how many ways can we paint the walls and ceiling of a pentagonal room if adjacent walls, and any wall and the ceiling, are to be painted with different colors?
(ii) What is the smallest value of k for which such a coloring is possible?
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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