3. a. Define the following with an example;i. pathsii. simple graphb. Draw the graph with the adjacency matrixго321311with respect to the11L212ordering of vertices, a, b, c, d.i. Find the degree of each vertex in your graph frompart (a) above.ii. How many walks of length 2 are there from thevertex c to c? How many of these walks are paths? LECTURER: Edwin Mireku4. a. Define the following Terms giving one exampleeach:i. Partial Ordering Relationsii. Equivalence relationsb. Answer these questions for the partial orderrepresented by the following Hasse diagram.ad1Smbi. Find the maximal elements.ii. Find the minimal elements.iii. Is there a greatest element?iv. Is there a least element?V.Find all upper bounds of {m, k, s}.vi. Find all lower bounds of {c, d, t}.vii. Find the greatest lower bound of {u, k, m} if itexists.viii. Find the least upper bound of {b, k, t} if itexists.

Answered: Image /qna-images/answer/3d6ff88b-1178-4208-b28f-85e3f1522933.jpg

Answered: paths simple graph

Math

Advanced Math

paths simple graph

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.3: Logarithmic Functions And Their Graphs

Problem 137E

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Question

100%

3. a. Define the following with an example;
i. paths
ii. simple graph
b. Draw the graph with the adjacency matrix
го
3
21
3
1
1
with respect to the
1
1
L2
1
2
ordering of vertices, a, b, c, d.
i. Find the degree of each vertex in your graph from
part (a) above.
ii. How many walks of length 2 are there from the
vertex c to c? How many of these walks are paths?

LECTURER: Edwin Mireku
4. a. Define the following Terms giving one example
each:
i. Partial Ordering Relations
ii. Equivalence relations
b. Answer these questions for the partial order
represented by the following Hasse diagram.
a
d
1
S
m
b
i. Find the maximal elements.
ii. Find the minimal elements.
iii. Is there a greatest element?
iv. Is there a least element?
V.
Find all upper bounds of {m, k, s}.
vi. Find all lower bounds of {c, d, t}.
vii. Find the greatest lower bound of {u, k, m} if it
exists.
viii. Find the least upper bound of {b, k, t} if it
exists.

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