Chapter 8, Problem 60E

Symmetric and totally asymmetric digraphs. A digraph is called symmetric if, whenever there is an arc from vertex X to vertex Y, there is also an arc from vertex Y to vertex X. A digraph is called totally asymmetric if, whenever there is an arc from vertex X to vertex Y, there is not an arc from vertex Y to vertex X. For each of the following, state whether the digraph is symmetric, totally asymmetric, or neither.

a. A digraph representing the streets of a town in which all streets are one-way streets.

b. A digraph representing the streets of a town in which all streets are two-way streets.

c. A digraph representing the streets of a town in which there are both one-way and two-way streets.

d. A digraph in which the vertices represent a group of men, and there is an arc from vertex X to vertex Y if X is a brother of Y.

e. A digraph in which the vertices represent a group of men, and there is an arc from vertex X to vertex Y if X is the father of Y.