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Nov Dec 2018.pdf-Total No. of Questions— 8 ]

Nov_Dec_2018.pdf-Total No. of Questions— 8 ]

Nov Dec 2018.pdf-Total No. of Quest...

Nov_Dec_2018.pdf-Total No. of Questions— 8 ]

##### Page 4

[5459]-181

4

5.

(

a

)

Find maximum flow in the transport network using labeling

procedure. Determine the corresponding min cut :

[7]

(

b

)

Define the following terms :

[6]

(

i

)

Level and height of a tree

(

ii

)

Cut points

(

iii

)

Eccentricity of a vertex.

Or

6.

(

a

)

Find minimum spanning tree for the graph shown below using

Kruskal’s algorithm.

[7]

(

b

)

Suppose data items A, B, C, D, E, F, G occur in the following

frequencies respectively 10, 30, 5, 15, 20, 15, 5. Construct a

Huffman code for the data. What is the minimum weighted

path length ?

[6]

CEGP013091

49.248.216.238 01/12/2018 09:26:37 static-238

CEGP013091

49.248.216.238 01/12/2018 09:26:37 static-238

CEGP013091

49.248.216.238 01/12/2018 09:26:37 static-238

##### Page 5

[5459]-181

5

P.T.O.

7.

(

a

)

Let Z

n

= {0, 1, 2,

...........

,

n

– 1}. In Z

12

what is the order

of 3, 6 and 8.

[3]

(

b

)

Let (

Q

, *) is an Algebraic system. * is a binary operation

defined as

a

*

b

=

a

+

b

–

ab

a

,

b

Q. Determine

whether (Q, *) is a group.

[4]

(

c

)

Define :

[6]

(

i

)

Rings

(

ii

)

Integral domain

(

iii

) Field.

Or

8.

(

a

)

Let Z

n

= {0, 1, 2,

.........

,

n

– 1}. Let * be a binary operation

such that

a

*

b

= remainder of (

a

+

b

) divided by

n

.

Construct a table for

n

= 4. Is (Z

4

, *) a monoid, semigroup,

group and abelian group.

[7]

(

b

)

Define :

[6]

(

i

)

Group code

(

ii

)

Galois theory

(

iii

) Cyclic group.

CEGP013091

49.248.216.238 01/12/2018 09:26:37 static-238

CEGP013091

49.248.216.238 01/12/2018 09:26:37 static-238

CEGP013091

49.248.216.238 01/12/2018 09:26:37 static-238

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