3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit
3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit
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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![3. а)
Define the following terms as used in graph theory:
i)
regular graph
ii)
simple circuit
[1 1 2]
b)
Let A = |1 0 1 be the adjacency matrix for the graph G, with
[2 1 o]
vertices vi, v2, V3.
i)
Find the number of walks of length 2, from vi to vi.
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 vi. Which
ones are simple circuits?
1 01
0 0
represents the relations R defined o
1
1
1 1
1
c)
The matrix M:
11
-
the set A = {1, 2, 3, 4}.
i)
List the ordered pairs in the relation R.
ii)
Draw the graph representing the relation R.
d)
How many edges does a 50-regular graph with 100 vertices have?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc91eed7-256f-4408-a8fe-17b48206f807%2F1ee13a48-d32b-45ac-a1d4-ae8091f8ecf5%2Fr50pn82_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]
b)
Let A = |1 0 1 be the adjacency matrix for the graph G, with
[2 1 o]
vertices vi, v2, V3.
i)
Find the number of walks of length 2, from vi to vi.
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 vi. Which
ones are simple circuits?
1 01
0 0
represents the relations R defined o
1
1
1 1
1
c)
The matrix M:
11
-
the set A = {1, 2, 3, 4}.
i)
List the ordered pairs in the relation R.
ii)
Draw the graph representing the relation R.
d)
How many edges does a 50-regular graph with 100 vertices have?
![5. а)
Define the following with an example:
i)
Domain of a function
ii)
One – to – one function
4х +1
A function f is defined on the det of real numbers by f(x)=
2х -3
b)
i)
Write down the domain of f.
ii)
Show that f is a one – to – one function.
iii)
Find the inverse of the function f.
c)
Given the function f(x) = x², g(x) = 3x – 4, find the composite
function gof (where gofmeans f followed by g)
d)
A function fis defined on the set N of natural numbers by
A0) = 2, {2) = 5 and ſ(n) = 2 A(n - 1)+3 f(n - 2) + An - 3)
for all n 2 3. Find f(4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc91eed7-256f-4408-a8fe-17b48206f807%2F1ee13a48-d32b-45ac-a1d4-ae8091f8ecf5%2F27s5gk_processed.png&w=3840&q=75)
Transcribed Image Text:5. а)
Define the following with an example:
i)
Domain of a function
ii)
One – to – one function
4х +1
A function f is defined on the det of real numbers by f(x)=
2х -3
b)
i)
Write down the domain of f.
ii)
Show that f is a one – to – one function.
iii)
Find the inverse of the function f.
c)
Given the function f(x) = x², g(x) = 3x – 4, find the composite
function gof (where gofmeans f followed by g)
d)
A function fis defined on the set N of natural numbers by
A0) = 2, {2) = 5 and ſ(n) = 2 A(n - 1)+3 f(n - 2) + An - 3)
for all n 2 3. Find f(4).
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