Question

Show all work for full credit. PART A Graph Theorv). 01.a. Model the following problem into a graph coloring problem A local zoo wants to take visitors on animal feeding tours, and is considering the following tours: Tour 1 visits the monkeys, birds, and deer Tour 2 visits the elephants, deer and giraffes; Tour 3 visits the birds, reptiles and bears Tour 4 visits the kangaroos, monkeys and bears Tour 5 visits birds, kangaroos and pandas; Monday, Wednesday and Friday To answer this, model the following problem into a graph coloring problem and complete parts (i) and (i) (i) Draw a graph G with vertices as tours. What are the edges? What do the colors mean? GRAPH: (i) Show an assignment of the days for each of the tours 01(b) Define the chromatic polynomial P/(G) of any graph G. How can you find chromatic number x (G) from the chromatic pohynomial of a graph? Ql(c) Find the chromatic polynomial of the following tree on 7 vertices. (the tree is drawn as a rooted tree). Based on this, find the chromatic number of the tree? Give the order of the vertices in which you color the vertices). 4 aua) Find the Prüffer sequence for the following labeled tree. At every step say tshuch teaf is deleted Show twork 2

Answer 1

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