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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?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 74EQ
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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
Transcribed Image Text: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.
Transcribed Image Text:-. 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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