Algortithm & Graph Theory

8/6/2019 Algortithm & Graph Theory

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ALGORITHM & GRAPH THEORY

1. Finite set of instructions is called _______

a. Relation b. Function c. Algorithm* d. Flowchart

2. The word algorithm belongs to which author ______

a. English b. Parisian* c. British d. None

3. The expression of an algorithm is called ______a. Flowchart b. Algorithm c. Program* d. None

4. The field of study is _______a. Analysis* b. Design c. Implementation d. Testing

5. The algorithm is executed by ______

a. DMA b, CPU c. MU d. None

6. Process of executing is _______

a. Process b. Profile c. Debugging* d. Performance

7. Measuring the time of execution ______a. Profiling* b. Process c. Debug d. None

8. The size (or) number of inputs & outputs ________

a. Size b. Space* c. Time d. None

9. Space requirement s(p) ________

a. c + Sp* b. c-Sp c. c * Sp d. c/Sp

10. Time complexity is denoted by

a. T (p)* b. T(q) c. T (t) d. T (r)

11. The sum of compile time and execution time is _______

a. P* b. Q c. R d. None

12. The runtime is denoted by

a. t c b. t r c. t p* d. None

13. Execution time also called as ______

a. Compile time b. Run time* c. Both d. None

14. tp(n) =

a. Ca ADD (n) + Cs SUB (n) + Cm MUL (n) +Cd DIV (n) + .*

b. Ca ADD? (n) Cs SUB (n) * Cm MUL (n) Cd DIV (n) + ..c. Both d. None

15. The instance character of ADD is denoted by

a. Ca * b. Cs c. Cm d. Cd16. Comment count as _______ step

a. 1 b. 2 c. 3 d. 0*

Bhargavi Institute of Management and Technology, KPHB, Ph:-040-23068451

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17. The statement does not involve any calls, takes ______ stepsa. 0 b. 1* c. 2 d. Infinite

18. In laps we consider the steps

a. Initialize b. control part* c. Increment d. None

19. How many methods for determine the no. of slips

a. 0 b. 1 c. 2* d. 3

20. Steps for execution is denoted by _______

a. p/c b. q/c c. r/c d. s/c*

21. Frequency of the for statement ______

a. n b. n + 1* c. n + 2 d. n + 3

22. Asymptotic complexity is denoted by ______a. C b. c. d. All*

23. The function 3n + 2 is denoted by _______

a. O (n)* b. O (n2) c. O (n

3) d. None

24. The function 3n2 + 3n + 2 is denoted by _______

a. O (n) b. O (n2)* c. O (n

3) d. None

25. O (2n) is called _____

a. Linear b. Quadratic c. Cubic d. Exponential*

26. f (n) = O (g(n)) where g( n) is _____a. Lower bound b. Upper bound* c. Both d. None

27. f (n) = (g(n)) where g(n) is _______a. Lower bound* b. Upper bound c. Both d. None

28. f (n) = (g(n)) where g (n) is ______a. Lower bound b. Upper bound c. Both * d. None

29. Ordered list is called ______

a. stack b. Queue c. Both * d. None

30. Stacks are sometimes referred to as

a. LIFO* b. FIFO c. Both d. None

31. In stacks, the operation are made ______ end

a. Bottom b. Top * c. Both d. None


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32. In stacks, the insertion is called ______

a. PUSH* b. POP c. Both d. None

33. If Top = n-1

a. Empty b. No elements c. Full * d. Only one element

34. If Top = -1

a. Empty b. No elements c. Both a& b* d. None

35. In queues, the insertion possible at

a. Front end b. Rear* c. Both d. None

36. In queue, the deletion is possible at

a. Front end* b. Rear c. Both d. None

37. In queue, the front end is initialized to ______

a. f = 0* b. f = -1 c. f = n-1 d. None

38. In queue, the rear end is initialized to _____a. r = 0 b. r = -1* c. r = n -1 d. r = f

39. A finite set of one or more nodes _____a. Stack b. Queue c. Linked list d. Tree*

40. The maximum level of any node is _____a. Length b. Breadth c. Height d. a, c*

41. A function call itself is _____

a. Recursion* b. Argument c. Both d. None

42. Heap is a ______

a. Tree b. Binary Tree c. complete binary tree* d. Both b, c

43. In Heap Tree, the root nodes have alwaysa. Small value b. +ve value c. ve value d. Large value*

44. A data structure known as ______a. Stack b. Queue c. Heap d. Hashing*

45. Hashing is provide ______ searchinga. Slow b. Fast* c. Medium d. None

46. Computational procedures ______

i. Defective ii. Effective iii. Infinite iv. Finitea. Only i b. Only ii c. Both I and ii * d. All


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47. Testing means _____

i. Debugging ii. Profiling iii. Performance iv. Measurea. Only I b. Only ii c. Both I and ii * d. None

48. S (p) = C +Sp, C means _____

i. Constant ii. Coefficient iii. Co-relation iv. Couplea. Only I b. Only ii c. Both I and ii* d. None

49. How many steps takes the following algorithmAlgorithm sum (a, n)

{

S : =For I : = 1 to n do

S : = S + a [i] ;

Return S ;}

a. 2n + 1 b. 2n +2 c. 2n + 3* d. 2n

50. Match the following.1. O (i) Omega

2. (ii) Theta3. (iii) Oh

a. (1, i), (2, ii), (3, iii) b. (1, ii), (2, i), (3, iii)

c. (1, iii), (2, ii), (3, i) d. (1, iii), (2, i), (3, ii)*

51. All algorithms must satisfy the following criteria

Rearranging them.1. Definiteness 2. Input 3. Effectiveness 4. Finiteness 5. Outputa. 1,2,3,4,5 b. 2,5,1,4,3* c. 4,2,1,3,5 d. 1,2,4,5,3

52. Re-arranging the following data

1. Analyze algorithm 2. Test a program 3. Validate algorithm 4. Devise algorithm

a. 2, 3, 1, 4s b. 1, 2, 3, 4 c. 4, 3, 2, 1 d. 4, 3, 1, 2*

53. Match the following.

1. Sum i. Cs

2. Subtraction ii. Cd

3. Multiplication iii. Ca4. Division iv. Cm

a. (1, iii), (2, i), (3, iv), (4, ii) b. (1, i), (2, ii), (3, iii), (4, iv)c. (1, ii), (2, iii), (3, i), (4, iv) d. None

54. Give an sequential order1. O (n log n) 2. O (n

s) 3. O (1) 4. O (log n) 5. O (2n)

6. O (n) 7. O (n2)


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a. [n/2] b. [n

]* c. [n2/2] d. None


a. 1, 2,3, 4, 5, 6, 7 b. 7, 6, 5, 4, 3, 2, 1

c. 6, 2, 3, 5, 7, 1, 4 d. 3, 4, 6, 1, 7, 2, 5*

55. Find out the Heap Trees

(i) 90 (ii) 90 (iii) 90


5

80 70 80 70 70 80

40 45 35 50 40 45 50 30

a. Only I b. Only ii c. Only iii d. All*

1

2

n +

DIVIDE AND CONQUER1. The splitting process is called _______

a. Divide b. Combine c. Both * d. None

2. The condition of Divide and Conquer is _______a. 1


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iii.1n

2

+


11. Merge means ______a. Divide b. Combine* c. Both d. None

12. Which is the fastest sort

a. Bubble sort b. Merge sort c. Quick sort* d. None

13. Match the following data

1. T (n) = g(n) i. otherwise

2. T (n) = T (n1) + T (n2) + ... T (n k) ii. n is smalla. (1, i), (2, ii) b. (1, ii), (2, i) * c. Both a , b d. None

14. Match the following data.1. T (n) = T (1) i. n = 1

2. T (n) = a, (r/b) + f (n) ii. n>1

a. (1, i), (2, ii)* b. (1, ii), (2, i) c. Both a, b d. None

15. Match the following data1. Successful search i. 1 + 1/n

2. Unsuccessful search ii. E / n+1

a. (1, i), (2, ii)* b. (1, iii), (2, i)s c. (2, iii), (1, ii) d. None

16. Match the following data.

. 1. T (n) = g (n) i. n > 12. T (n) = T (n1) + T (n2) + ..+ T (n2) ii. n small

3. T (n) = 2 T (n/2) + f (n) iii. n 2

2. T (n) = 1 (ii). n = 23. T (n) = 0 (iii). n = 1

a.(1, i), (2, ii), (3, iii)* b. (1, iii), (2, ii), (3, i) c. (1, ii), (2, i), (3, iii) d. None

Greedy Method

1. Subset of solutions satisfies some constraints is called ______


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a. 1 I n t s* b. 1< I < n t s c. n 1 I n t s d. None


a. feasible solution* b. optimal solution c. both d. None

2. A feasible solution that either max or min object function ____

a. feasible solution b. optimal solution* c. both d. None

3. Usually an obvious way to determine _______ solutiona. feasible * b. optimal c. both d. None

4. for determining the optimal solution ______ methoda. Greedy* b. Greenburg c. Gassordon d. None

5. Input is added to ______ solution (If input is feasible)a. feasible b. optimal c. partial* d. None

6. In Greedy method, what is paradigm?a. select b. feasible c. union d. all*

7. ______selects an input from array and removes it

a. select* b. feasible c. union d. all

8. _____ id determines whether x can be induced into the solution veet

a. select b. feasible* c. union d. all

9. _____ combines x with the solution and updates

a. select b. feasible c. union* d. all

10. Greedy method is also called as _____a. order b. paradigm c. both a, b d. ordering paradigm*

11. MRT stands for ______a. Meridian Time b. Mean Rate time

c. Minimum Rate time d. Mean retrieval time*

12. Each program I is a length l, condition is ______a. 1 I n* b. 1< I < n c. 1 I < n d. 1< I n

13. MRT =1

n

14. MRT is equivalent to minimizing d(l) =

a. 1 j n 1 k j l Ik* b. 1 < j n 1 < k n l Ik c. Both a, b d. None

15. Increasing the d value by

a. 1 j n l Ik + l j b. 1 < j n l Ik l j c. Both a, b d. None


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16. Total retrieval time (TD) _______

a. o < j m 1d (l j ) b. o < j m + 1d (l j ) c. o j m 1d (l j )* d. All

17. The general rule is that program I is stored on tape _______

a. T5 mod m b. TJ mod n c. T I mod n d. T I mod m*

18. Knapsack problem maximize is

a. 1 I n p i x I * b. 1 I n w i x I c. Both d. None

19. Knapsack algorithm required _______ time

a. O (1) b. O (n log n) c. O (log n) d. O (n)*

20. Greedy algorithm for sequencing unit time jobs witha. deadlines b. profits c. both a & b* d. None

21. The worst case computing time for Js isa. O (n

2) b. ( n2 ) c. (s)* d. All

22. Js needs _____ amount of space for J

a. O (s) b. (s) c. (s)* d. All

23. Merging mean _____

a. Combine two files b. combine two or more filesc. combine two sorted files d. combine two or more sorted files*

24. Merging an n-record file and an m-record file requires possible

a. n + m* b. n-m c. nm d. None


1. Storage on tapes i. o (n log n) time

2. Knapsack problem ii. ( n2 ) time (a asymptotic)3. Optimal merge iii. ( n2 ) time4. shortlist path iv. ( n ) time

a. (1, I), (2, ii), (3, iii), (4, iv) b. (1,iv), (2, iii), (3, ii), (4, i)

c. (1, ii), (3, i), (4, iii), (2, iv) d. (1, iv), (2, iii), (3, i), (4, ii)*

26. Find the optimal ordering for the optimal storage on tapes.N = 3, (l1, l2, l3) (5, 10, 3)

a. 38 b. 41 c. 26 d. 29*

27. What is the shortest path in the following diagram: (form vertex 1 to 3)


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50 101 2 3

9

15 35

10 20 20 30

4 5 6

15 3

a. 25 b. 35 c. 45* d. 55

28. Find the feasible solutions for the following jobN = 4, (P1, P2, P3, P4) = (100,10,15,15,27) & (d1, d2, d3, d4) = ( 2, 1

a. 100 & 27 b. 100 & 15 c. 100 & 10* d. All

29. Find the feasible solutions for the following knapsackN = 3, m = 20 (P1, P2, P3, P4) = (25, 24 ,15)

And (W1, W2, W3) = (18, 15, 10)

a. 10 b. 20 c. 30 d. None*

Dynamic Programming

1. This method is used for ______a. One decision b. sequence of decision* c. Two d. None

2. Decision sequences containing subsequence that are suboptimal are not ____

a. Consider* b. Solution c. Not solution d. None

3. The total no. of different decision sequences to _______

a. Power b. Square c. Logarithmic d. Exponential*

4. Dynamic programming algorithms often have a _____a. Dynamic complexity b. Polynomial complexity* c. Both d. None

5. Dynamic programming approach is ______a. Detect recomputing b. Avoid recomputing value* c. Both d. None

6. In multistage graph, the vertices are partitioned intoa. K 2 b. K < 2 c. K > 2 d. K 2*

7. The multistage graph is to find ______

a. Maximum cost b. Minimum cost* c. Both d. None

8. Resource allocation problem saving ______ stages



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a. r b. r-1 c. r + 1 * d. None

9. Cost (i, j) = min {

a. C (j, l) cost (i+1, l) b. c (j, l) x cost (i + l, l) c. c (j, l) + cost (i + l, l)

10. All pair shortest paths A (I, j) =a. min { min 1 k n { Ak 1

(I , k) + Ak 1

(k, j) } cos (i, j)*

b. min { min1 k n { Ak 1

(I , k) - Ak 1

(k, j) }

c. min { min 1 k n { Ak 1

(I , k) * Ak 1

(k, j) }d. None

11. All pair shortest path solved by ______a. n b. n c.

n*

d. None

12. In all pair shortest path, time for all paths

a. (n) b. ( n2 ) c. ( n3 )* d. ( n4 )

13. Traveling salesman problem for finding ______a. Minimum cost * b. Max c. Both d. None

14. The main drawback of Dynamic problem is ______a. O(n) b. O (2n) c. O (2n) d. O (n 2

n)

15. Dynamic programming applicable fori) Multistage graphs ii) All pair shortlist paths iii) Traveling salesman problems


16. Match the following data.1. for j: = n-1 to K step-1 do i. ( |V| + |E| )2. for j : = 2 to -1 do p [j]: = d [ p (j-1)] ii. ( |V| + |E| )3. Total time iii. (K)

a. (1, i), (2, ii), (3, iii) b. (1, i), (2, iii), (3, ii)* c. (1, iii), (2, ii), (3, i)

17. Drawback of dynamic program is ______i) n ii) 2

niii) n.2

niv) All

a. Only I b. Only ii c. Only iii* d. None

18. In all pair shortest path iterated _____ timei) n ii) n iii) n d. None

a. Only I b. Only ii c. Both I & ii d. Only iii*

Backtracking

1. Searching for a set of solutions ____


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a. Greedy Method b. Dynamic programming c. Backtracking* d. None

2. The name backtrack was first coined by

a. D Lehmer b. D. H. Lehmer* c. H. Lehmer d. None

3. The name backtrack was ina. 1930 b. 1940 c. 1950 * d. 1960

4. The backtrack method, the desired solution to ______ tuplesa. n * b. n 1 c. n + 1 d. None

5. A collection of problems whose solution are best done using ______a. Greedy b. Dynamic c. Backtracking * d. All

6. In 8-Queens problem, solution space consist of ____ tuples

a. 8 x 8 b. 88

c. 8 ! d. None

7. Reduce the size of the space 88

to ______

a. 8 x 8 b. 88

* c. 8 ! d. None

8. For an 8 x 8 chessboard there are _____ possible ways

a. 64p8 b. 64c8 * c. 64 x 8 d. 8 x 64

9. The total roof nodes in the 8 queen static space isa. 69280 b. 69281 c. 69282 d. None

10. Sum of subsets are represented in ______a. Binary* b. Decimal c. Octal d. Hexadecimal

11. If n=4, then the tree having _____ no. of leaf nodes

a. 2 x 4 b. 4 c. 2/4 d. 24*

12. In knapsack problem, m is denoted _______

a. Capacity* b. Weight c. Profit d. None

13. Knapsack problem having ______ways

a. 2 x n b. n ! c. 2! D. 2n

14. The Backtracking method is applicable for ______i) 8 queen problem ii) sum of subjects iii) knapsack problem


15. Backtracking having ______ constraints

I) Explicit ii) Implicit iii) Equal

a. Only I b. Only ii c. Both I & ii* d. None


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a. b.

10 17 0 1

12 11 2 0

0 3 0 2

15 3 12 0

11 0 0 12

*


16. n = 4, m = 3 and (W1, W2, W3, W4) = (11, 13, 24, 7) having ______ subseti) 1 ii) 2 iii) (11, 37), (24, 7)

a. Only I b. Only ii c. Both ii & iii * d. Only iii

17. The solution of 8-queen problem isa. (2, 7, 1, 4, 3, 5) b. (1, 4, 2, 6, 8, 7, 5)

c. (4, 6, 8, 2, 7, 1, 5, 3) d. (4, 6, 8, 2, 7, 1, 3, 5)*

BRANCH AND BOUND

1. Branch and bound refers to ______

a. one state space b. two sate space c. Three d. All state space*

2. Bounding functions are used for to avoid ______

a. Tree b. Subtree* c. Both a & b d. None

3. BFS (Breads First Search ) like ______a. FIFO* b. LIFO c. Both a & b d. None

4. DFS (Depth First Search ) like _____a. FIFO b. LIFO* c. Both a & b d. None

5. _____ technique is sure any problema. Greedy b. Dynamic program c. backtracking d. Branch and bound*

6. The Drawback of Dynamic program solved by ______a. Greedy b. Dynamic program c. backtracking d. Branch and bound*

7. Branch and bound used for

i) Knapsack problem ii) Traveling salesman

a. Only I b. Only ii c. Both I & ii* d. None

8. The reduced cost Matrix of the following cost Matrix is _______20 30 10 11

5 16 4 2

3 5 2 4

9 6 18 3

16 4 7 16

( 2)

2

n n +

c. No solution d. None

9. What is the minimum cost of the following cost Matrix.


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13

2

20 30 10 11

5 16 4

3 5 2 4

9 6 18 3

16 4 7 16

a. 25 * b. 35 c. 52 d. 53

Additional Features

1. _____ is the lower bound on time for any algorithm

a. f(n) = O (g(n)) b. f(n) = (g(n))* c. (n) = (g(n)) d. None

2. In general, _____ is the lower bound for any algorithma. O (n) b. (n) * c. (n) d. None

3. _____ trees are used for comparison for searching & sortinga. Tree b. Binary tree* c. Complete binary tree d. None

4. The time complexity for searching FIND (n) is

a. log n b. log n 2 c. log n+1 d. log n3

5. The time complexity for sorting T (n) is

a. log n !* b. log n+1 c. log n d. None

6. Cooks theorem sates that p =

a. N b. P c. NP* d. None

7. A k-clique in a graph in a graph G is a complete sub-graph of G with ______ vertices

a. K * b. 5 c. 2 d. All

8. K-clique problem is

a. NP hard b. NP complete c. Both d. None

9. Approximate algorithm fora. NP complete b. NP hard* c. Constant d. All

10. E approximate algorithms for ____

a. NP complete b. NP hard c. Constant* d. None

11. _____ algorithm for p |F (l) F (l) |

K (K is constant)a. Approximate b. E- approximate* c. Both d. None

12. The time complexity of planar graph colouring is _____

a. O (|V|) b. O (|E|) c. O (|V| + |E|) * d. O (|V| _ |E|)

13. _____ time is needed to obtain the storage assignment

a. O (n)* b. O (n2) c. O (n

3)d. O (n

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14. Bin packing for finding the_______a. Constant bins b. Minimum bins* c. Maximum bins d. All

15. Planar graph coloring is an ______ algorithm

a. NP complete b. NP hard* c. Both d. None

16. Bin packing is _____ algorithm

a. NP complete b. NP hard c. Both d. None

17. Cluster having ______ types

i) Polynomial ii) Non -polynomiala. Only I b. Only ii c. both I & ii* d. None

18. Match the following.1. Traveling salesman i. O (n

22

n)

2. Knapsack problem ii. O (2

n/2

)a. (1, i), (2, ii) b. (1, ii), (2,i) c. Both * d. None

19. Which program are disk1 & disk2

L = 10, n = 4 (l1, l2, l3, l4) = (2, 3, 4, 5)

i) 1 & 2 on disk1 & 3 on disk2

ii) 1 & 3 on disk1 & 2 on disk2

iii) 1 & 4 on disk1 & others on disk2

a. Only I b. Only ii c. Both I & ii d. Only iii*

20. What is the finishing time

M = 3, n = 2, (t1, t2, t3, t4, t5, t6) = (8, 7, 6, 5, 4, 3)

a. 10 b. 11* c. 12 d. None

21. Arrange the following NP hard problems A/c to text1. Bin packing 2. Planar graph coloring

3. t approximation 4. Polynomial time approx

a. 1, 2, 3, 4 b. 4, 3, 2, 1 c. 2, 1, 4, 3 d. 2, 3, 1, 4*

Graphs1. A set of vertices and Edges is called _______

a. Graph* b. Planar c. Euler d. None

2. Diagraph itself is referred to asa. Planar b. Graph* c. Euler d. None

3. An edge having the same vertex as its end vertices is called


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a. b. 2n n

c. 3n n +

d.( 1)

3

n n *


a. Double loop b. triple bond c. Self loop* d. None

4. Allows more than one edge associated with a giver pair of vertices

a. Self edges b. Edges c. Cross edges d. Parallel edges*

5. A graph has no self-loop or parallel edger is calleda. Simple graph* b. Multiple graph c. Non-simple d. None

6. A graph has every edge (a b) there is also an edge (b, a) is called _____a. Asymmetric b. Symmetric* c. Diagraph d. None

7. Every vertex is joined to every other vertex is called ______a. Cycle b. Path c. Complete* d. Bipartite

8. a walk is also referred to as an edge train or a chain _______a. Cycle b. Complete c. Bipartite d. Path*

9. In path, we have _____ types

a. 2* b. 3 c. 4 d. None

10. A closed walk, no vertex appear more than once

a. Cycle b. Circuit* c. Path d. None

11. The no. of edges on a vertex is called ______

a. Indegree b. Outdegree c. Degree* d. None

12. A complete graph has no. of edges is ______( 1)

2

n n + ( 2)+ ( 1)

13. At least one path between every pair of vertex in G _____

a. Connectivity* b. Relation c. Conjunction d. None

14. An edge whose removal disconnects the graph ______a. Path b. Bridge* c. Block d. None

15. The largest non-separable sub graphs is calleda. Path b. Bridge c. Block* d. None

16. A connected graph without any circuits is ______a. Path b. Bridge c. Block d. Tree*

17. The sorting of Tree is called _______

a. Decision Tree b. Sorting Tree c. Both a & b* d. None

18. A tree with n vertices has _____ edges


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a. e n + 2* b. e + n + 2 c. e n 2 d. None

34. The painting of vertex is called ______

a. Painting number b. chromatic* c. Even d. Odd

35. The vertices of every planar graph can be properly colored witha. 3 color b. 4 color c. 5 color* d. None

36. Representation of Graph we have _____ typesa. 1 b. 2 c. 3* d. 4

37. The minimum length between two vertices is ______a. Shortest path b. Open path c. Closed path d. None

38. Which algorithm for labeling the vertices ______a. Kruskal b. Kurtosis c. Dijkstra* d. None

39. Mentioned the length of the edge is called ______

a. vertex label b. Edge label* c. Both d. None

40. Mentioned the length of all the edges is called ______

a. Graph b. Planar c. Non -weighted d. Weighted Graph*

41. Which algorithm for planarity _______

a. Kuratowski b. Dijskstra c. Both d. None

42. DETECTION for planarity is ______a. DFS b. BFS c. Both* d. None

43. DFS stands fora. Depth First Search b. Breath First Search c. Both d. None

44. Which algorithm used for finding the DFS

a. kuratowski b. Disjkstra c. DES * d. None45. Circuit-path Decomposition for testing of ______

a. Planarity* b. Eater c. Hamiltonian d. None

46. Which algorithm to find a minimal spanning Tree

a. Kruskals* b. Kuratowski c. Dijskstra d. None

47. A sub-Tree having all the vertices of Tree T is called

a. Tree b. Sub-Tree c. Spanning Tree* d. Directed

48. Every Graph itself a _______a. Sub-graph * b. Spanning c. Both d. None


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49. Asymmetric diagraph is also called as ______

a. Tournament b. Complete tournament c. Both a, b* d. None


1. Indegree (i) Towards vertex

2. Outdegree (ii) Outwards vertex

a. (1, i), (2, ii)* b. (1, ii), (2, i) c. Both d. None


1. Indegree (i) dt(v)

2. Outdegree (ii) d (v)3. Degree (iii) d

(v)

a. (1, i), (2, ii), (3, iii) b. (1, iii), (2, ii), (3, i) c. (1, i), (2, iii), (3, ii)* d. None

52. Match the following.1. Graph (i) Linear complex, 1 complex, 1 dimensional

2. Vertex (ii) node, function, point, o cell, o simplex3. Edge (iii) branch, line, element, 1 cell, arc, a- som

a. (1, i), (2, ii), (3, iii)* b. (1, iii), (2, ii), (3, i) c. (1, i), (2, iii), (3, ii) d. None


1. Vo = Vn (i) Initial vertex2. Vo = Vn (ii) Closed path

3. Vo (iii) Final vertex4. Vn (iv) Open path

a. (1, i), (2, ii), (3, iii), (4, iv) b. (1, ii), (2, iv), (3, i), (4, iii)* c. None

54. Hamiltonian path means

(i) Exactly 1 vertex (ii) Exactly 1 edge (iii) Exactly 1 vertex

a. Only I* b. Only ii c. Only I and ii d. All55. The no. of possible choices Hamiltonian circuits in a Graph

(i) (n 1)! (ii) n 1 (iii) (n 1)! /2

a. Only I* b. Only ii c. Both I and ii d. None

56. Chromatic number of bipartite Graph is(i) depend on no. of vertices (ii) only 2 (iii) 1 less no. of vertices

a. Only I b. Only ii* c. Both I and ii d. None


1. Vertex edge (i) Adjacent Matrix


18


19/20


2. Vertex vertex (ii) Incident Matrix

a. (1, i), (2, ii) b. (1, ii), (2, i)* c. Both d. None

58. Detection of planarity

(i) DFS (ii) BFSW (iii) Both I and ii

a. Only I b. Only ii c. Only iii* d All


1. Simple Graph (i) Vt = Vn

2. Non simple (ii) having multiple edges between two3. Multiple (iii) self loop

4. Cycle (iv) without self loop

a. (1, i), (2, ii), (3, iii), (4, iv) b. (1, iv), (2, iii), (3, ii), (4, i)c. (1, iv), (2, iii), (3, ii), (4, i) d. None


1. Cycle (i)


19

2. Wheat (ii) : :

3. Null (iii)

4. b partite (iv)

5. Complete

a. (1, iii), (2, iv), (3, ii), (4, v), (5, i)* b. (1, i), (2, ii), (3, iii), (4, iv), (5, v)

c. (1, ii), (2, i), (3, iii), (4, iv), (5, v) d. None


1. Complete graph (i) mn edges

2. Tree (ii) n (n -1 ) /2 edges3. b : partite Graph Kmn (iii) (n 1) edges

a. (1, i), (2, ii), (3, iii) b. (1, iii), (2, ii), (3, i) c. (1, ii), (2, iii), (3, i)* d. None


1. Eaters Formula (i) (p 2)2. Sum of all angles (ii) )p + 2)

3. Sum of interior angles (iii) 2 n

4. Sum f exterior angles (iv) e n + 2

a. (1, iv), (2, iii), (3, i), (4, ii)* b. (1,i), (2, ii0, (3, iii), (4, iv)

c. (I, i), (2, iv), (3, ii), (4, iii) d. All


20/20

a. b. c. d. None*

0 0 1

1 0 1

1 0 0


63. Arranging the following data in sequential1. Triangle is 3 chromatic 2. isolate vertex is 1 chromatic

3. one or more vertex is 2 chromatic

a. 1, 2, 3 b. 3, 2, 1 c. 2, 1, 3 d. 2, 3, 1*

64. Match the chromatic polynomial

1. C1 (i) 5!2. C2 (ii) 6

3. C3 (iii) 24

4. C4 (iv) 485. C5 (v) 0

a. (1, i), (2, ii), (3, iii), (4, iv), (5, v) b. (1, v), (2, iv), (3, ii), (4, iv), (5, i)c. (1, v), (2, iv), (3, iii), (4, ii),(5, i) d. None

65. Incident Matrix of the following graph


20

V1 E1 V2

E3 E2V3

1 0 0

0 1 0

0 0 1

0 0 1

1 0 1

1 0 0

66. What is the Minimal path in the above Diagram

a. (b, c), (d, f), (a, g), (c, d), (c, e), (a, b), (f, h) b. (b, c), (d, f), (a, g), (c, d), (c, e),(a, b), (g, h)

c. Both a and b* d. None

67. What is the Minimum cost of the following Diagram?

a 15 b

5

15 5 3

g 18 d c

15 4 5h 15 f 15 e

a. 25 b. 52* c. 225 d. 252

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Algortithm & Graph Theory