3. a. Define the following with an example; i. paths ii. simple graph 27 1 b.Draw the graph with the adjacency matrix 1 with 2 respect to the 1 1 12 1 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? 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 og i. Find the maximal elements. ii. Find the minimal elements. iii. Is there a greatest element? iv. Is there a least element?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. a. Define the following with an example;
i. paths
ii. simple graph
3
21
1
1
with respect to the
b.Draw the graph with the adjacency matrix
1
1
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?
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.
e
a
d'
m
'k
i. Find the maximal elements.
ii. Find the minimal elements.
iii. Is there a greatest element?
iv. Is there a least element?
오302
Transcribed Image Text:3. a. Define the following with an example; i. paths ii. simple graph 3 21 1 1 with respect to the b.Draw the graph with the adjacency matrix 1 1 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? 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. e a d' m 'k i. Find the maximal elements. ii. Find the minimal elements. iii. Is there a greatest element? iv. Is there a least element? 오302
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