3. a. Define the following with an example: i. paths ii. simple graph 0- 3. 2- b.Draw the graph with the adjacency matrix 1 3. 1 with respecct to the ordering of vertices, a, b, c, d. i. Find the degree of each vertex in your graph from part (a) above. 11. 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. 1 S m k b r n h i. Find the maximal elements. ii. Find the minimal elements. iii. Is there a greatest element? iv. Is there a least element?

3. a. Define the following with an example: i. paths ii. simple graph 0- 3. 2- b.Draw the graph with the adjacency matrix 1 3. 1 with respecct to the ordering of vertices, a, b, c, d. i. Find the degree of each vertex in your graph from part (a) above. 11. 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. 1 S m k b r n h 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

Section: Chapter Questions

Problem 1RQ

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Question

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a. Define the following with an example:
i. paths
ii. simple graph
3.
21
b.Draw the graph with the adjacency matrix
1
with respect to the
2.
0.
-2
ordering of vertices, a, b, c, d.
: Find the degree of each vertex in your graph from part (a) above.
1. 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
u
d'
m
k
h
i. Find the maximal elements.
ii. Find the minimal elements.
iii. Is there a greatest element?
iv. Is there a least element?
60
2110O
3011

-. Find all upper bounds of {m, k, s}.
i. Find all lower bounds of {c, d, t}.
i. Find the greatest lower bound of {u, k, m} if it exists.
ii.
Find the least upper bound of {b, k, t} if it exists.

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