3. a) Define the following terms as used in graph theory: i) regular graph ii) simple circuit [1 1 21 Let A = |1 0 1 be the adjacency matrix for the graph G, with l2 1 0. b) vertices vi, v2, V3. Find the number of walks of length 2, from vị to vị. Draw the graph G and label the edges e, (i = 1, 2, 3, ...) iii) i) ii) Write down the walks of length 2 from vị to vị. Which ones are simple circuits? [1 1 1 01 0 1 c) The matrix M = 8 : represents the relations R defined c 00 1 1 0 1 li o o 1] 0 0 the set A = {1, 2, 3, 4}. i) List the ordered pairs in the relation R. ii) Draw the graph representing the relation R. How many edges daes a 50-regular graph with 100 vertices have2
3. a) Define the following terms as used in graph theory: i) regular graph ii) simple circuit [1 1 21 Let A = |1 0 1 be the adjacency matrix for the graph G, with l2 1 0. b) vertices vi, v2, V3. Find the number of walks of length 2, from vị to vị. Draw the graph G and label the edges e, (i = 1, 2, 3, ...) iii) i) ii) Write down the walks of length 2 from vị to vị. Which ones are simple circuits? [1 1 1 01 0 1 c) The matrix M = 8 : represents the relations R defined c 00 1 1 0 1 li o o 1] 0 0 the set A = {1, 2, 3, 4}. i) List the ordered pairs in the relation R. ii) Draw the graph representing the relation R. How many edges daes a 50-regular graph with 100 vertices have2
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
![3. а)
Define the following terms as used in graph theory:
i)
regular graph
ii)
simple circuit
[1 1 2]
Let A =|1 0 1 be the adjacency matrix for the graph G, with
2 1 0
b)
vertices vi, v2, v3.
i)
Find the number of walks of length 2, from vị to vị.
ii)
Draw the graph G and label the edges e, (i = 1, 2, 3. ...)
iii)
Write down the walks of length 2 from vị to vị. Which
ones are simple circuits?
[1 1 1 01
0 10 0
0 0 1 1
li 0 0 1
c)
The matrix M = |8 : represents the relations R defined om
the set A = {1, 2, 3, 4}.
i)
List the ordered pairs in the relation R.
ii)
Draw the graph representing the relation R.
How many edges does a 50-regular granh with 100 vertices bave2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F364a3d18-5416-4cb1-ac78-52d1b02917d5%2Fc8b06db6-90b9-482f-bd64-5a6a39be2066%2Fkpeldw_processed.png&w=3840&q=75)
Transcribed Image Text:3. а)
Define the following terms as used in graph theory:
i)
regular graph
ii)
simple circuit
[1 1 2]
Let A =|1 0 1 be the adjacency matrix for the graph G, with
2 1 0
b)
vertices vi, v2, v3.
i)
Find the number of walks of length 2, from vị to vị.
ii)
Draw the graph G and label the edges e, (i = 1, 2, 3. ...)
iii)
Write down the walks of length 2 from vị to vị. Which
ones are simple circuits?
[1 1 1 01
0 10 0
0 0 1 1
li 0 0 1
c)
The matrix M = |8 : represents the relations R defined om
the set A = {1, 2, 3, 4}.
i)
List the ordered pairs in the relation R.
ii)
Draw the graph representing the relation R.
How many edges does a 50-regular granh with 100 vertices bave2
Transcribed Image Text:4. ay
DEIIT IIC IUIIOWIIng teIS.
i)
POSETS
ii)
Equivalence relation
b)
Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A
as follows:
For every (x. y ) eA,
XRy + 5 divides (x² - y³) and
XSy у - 1%3Dх
i)
List all the ordered pairs (x. y) in the relation R and S.
ii)
iii)
SOR (The composite relation R followed by S)
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