graphs

graphs

1) An intersection graph of a collection of sets A(1), A(2),…, A(n) is

the graph that has as a vertex each of these sets and has an

edge connecting the vertices representing two sets if these sets

have a nonempty intersection. The attachment contains an

example of an intersection graph for five sets A, B, C, D and E. Is

it possible to represent the graph as a relation? If yes, what

properties of relations would it satisfy?

2) An acquaintanceship graph can be use to represent relationships

between people for example whether two people know each

other. The individuals are represented by vertices and an

undirected edge means that the people know each other. An

example of such a graph can be found in the attachment. Use the

graph to provide an example of a “walk”, closed walk, a path and

a circuit.

3) Suppose we have the following algebraic expression:

[(x + y)^2]+[(x – 4)/3]. How can we represent this as a tree?

4) Suppose we are given a rooted tree, represented as T. Provide an

example of a tree and an algorithm which can be used to traverse

it.