3. а)Define the following terms as used in graph theory:i)regular graphii)simple circuit[1 1 2]Let A =|1 0 1 be the adjacency matrix for the graph G, with2 1 0b)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. Whichones are simple circuits?[1 1 1 010 10 00 0 1 1li 0 0 1c)The matrix M = |8 : represents the relations R defined omthe 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 4. ayDEIIT IIC IUIIOWIIng teIS.i)POSETSii)Equivalence relationb)Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on Aas follows:For every (x. y ) eA,XRy + 5 divides (x² - y³) andXSy у - 1%3Dхi)List all the ordered pairs (x. y) in the relation R and S.ii)iii)SOR (The composite relation R followed by S)

3) a. To define the terms regular graph and simple circuit. b. Let A=112101210 be adjacency matrix…

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

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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