Discrete Math Lesson 8.2 – Directed Graphs Exercise 1

Name ______________________________ Period ___________

Digraph – ____________________________________________________________________ ______________________________________________________________________________ A digraph is useful when _________________________________________________________ ______________________________________________________________________________ The classic example of an asymmetric relationship is love. Given two persons, X and Y, and the relationship love, we have four possible scenarios: (a) (b) (c) (d)

X

Y

X

Y

X

Y

X

Y

______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________

Arc - _________________________________________________________________________ Every arc is defined by its ________________________________________________________ -

XY describes graph __________ above.

-

YX describes graph __________ above

Arc-set - ______________________________________________________________________ -

The arc-set in graph (d) above is A = { _______, _______ }

In arc XY, we can say that vertex _______ is incident to vertex _______. Or we can say that vertex _______ is incident from vertex _______. Adjacent arcs - ________________________________________________________________ ______________________________________________________________________________ X

Y

Z

Path – In a graph, the path from vertex X to vertex W is a _______________________________ XY, YZ, ZU,…, XY, such that (1) ___________________________________________________ and (2) _______________________________________________________________________ X

Y

U

Z

V

W

Cycle - _______________________________________________________________________ ______________________________________________________________________________ Outdegree - ___________________________________________________________________ ______________________________________________________________________________ Indegree - ___________________________________________________________________ ______________________________________________________________________________ B

Exercise. Refer to the digraph in Figure 1. 1. What is the vertex set?

V = { ____________________ }

2. What is the arc-set for this digraph? A = { ______________________________________ }

C A

3. Vertex A is incident __________ vertex B.

D

Vertex B is incident __________ vertex A. Vertex D is incident __________ vertex E. E

Vertex E is incident __________ vertex D.

4. Arc AB is adjacent to arcs ______________________________________________________ 5. Identify all paths from vertex A to vertex D. 6. Identify the cycle in the digraph. __________________________ 7. Complete the table.

Vertex A B C D E

Outdegree

Indegree