MCQOPTIONS
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MCQOPTIONS
This section includes 99 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
The chromatic number of a graph is the property of ____________ |
| A. | graph coloring |
| B. | graph ordering |
| C. | group ordering |
| D. | group coloring |
| Answer» C. group ordering | |
| 52. |
In a poset (S, ⪯), if there is no element n∈S with m |
| A. | an element n exists for which m=n |
| B. | An element m is maximal in the poset |
| C. | A set with the same subset of the poset |
| D. | An element m is minimal in the poset |
| Answer» C. A set with the same subset of the poset | |
| 53. |
In a poset P({v, x, y, z}, ⊆) which of the following is the greatest element? |
| A. | {v, x, y, z} |
| B. | 1 |
| C. | ∅ |
| D. | {vx, xy, yz} |
| Answer» B. 1 | |
| 54. |
G is an undirected graph with n vertices and 26 edges such that each vertex of G has a degree at least 4. Then the maximum possible value of n is ___________ |
| A. | 7 |
| B. | 43 |
| C. | 13 |
| D. | 10 |
| Answer» D. 10 | |
| 55. |
In which of the following relations every pair of elements is comparable? |
| A. | ≤ |
| B. | != |
| C. | >= |
| Answer» B. != | |
| 56. |
An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8? |
| A. | 15 |
| B. | 8 |
| C. | 5 |
| D. | 23 |
| Answer» C. 5 | |
| 57. |
If the partial order of a set has at most one minimal element, then to test whether it has a non-crossing Hasse diagram its time complexity __________ |
| A. | NP-complete |
| B. | O(n²) |
| C. | O(n+2) |
| D. | O(n³) |
| Answer» B. O(n²) | |
| 58. |
Which of the following relation is a partial order as well as an equivalence relation? |
| A. | equal to(=) |
| B. | less than(<) |
| C. | greater than(>) |
| D. | not equal to(!=) |
| Answer» B. less than(<) | |
| 59. |
Hasse diagrams are first made by ______ |
| A. | A.R. Hasse |
| B. | Helmut Hasse |
| C. | Dennis Hasse |
| D. | T.P. Hasse |
| Answer» C. Dennis Hasse | |
| 60. |
A trail in a graph can be described as ______________ |
| A. | a walk without repeated edges |
| B. | a cycle with repeated edges |
| C. | a walk with repeated edges |
| D. | a line graph with one or more vertices |
| Answer» B. a cycle with repeated edges | |
| 61. |
Let a graph can be denoted as ncfkedn a kind of ____________ |
| A. | cycle graph |
| B. | line graph |
| C. | hamiltonian graph |
| D. | path graph |
| Answer» B. line graph | |
| 62. |
A ______ in a graph G is a circuit which consists of every vertex (except first/last vertex) of G exactly once. |
| A. | Euler path |
| B. | Hamiltonian path |
| C. | Planar graph |
| D. | Path complement graph |
| Answer» C. Planar graph | |
| 63. |
A walk has Closed property if ____________ |
| A. | v₀=vₖ |
| B. | v₀>=vₖ |
| C. | v < 0 |
| D. | vₖ > 1 |
| Answer» B. v₀>=vₖ | |
| 64. |
The sum of an n-node graph and its complement graph produces a graph called _______ |
| A. | complete graph |
| B. | bipartite graph |
| C. | star graph |
| D. | path-complement graph |
| Answer» B. bipartite graph | |
| 65. |
In a directed weighted graph, if the weight of every edge is decreased by 10 units, does any change occur to the shortest path in the modified graph? |
| A. | 209 |
| B. | 65 |
| C. | 57 |
| D. | 43 |
| Answer» D. 43 | |
| 66. |
Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph? |
| A. | topological sort |
| B. | hash table |
| C. | binary search |
| D. | radix sort |
| Answer» B. hash table | |
| 67. |
Determine the edge count of a path complement graph with 14 vertices. |
| A. | 502 |
| B. | 345 |
| C. | 78 |
| D. | 69 |
| Answer» D. 69 | |
| 68. |
A graph is ______ if and only if it does not contain a subgraph homeomorphic to k₅ or k₃,₃. |
| A. | bipartite graph |
| B. | planar graph |
| C. | line graph |
| D. | euler subgraph |
| Answer» C. line graph | |
| 69. |
The _______ of a graph G consists of all vertices and edges of G. |
| A. | edge graph |
| B. | line graph |
| C. | path complement graph |
| D. | eulerian circuit |
| Answer» E. | |
| 70. |
Let G(V, E) be a directed graph where every edge has weight as either 1, 2 or 5, what is the algorithm used for the shortest path from a given source vertex to a given destination vertex to get the time complexity of O(V+E)? |
| A. | BFS |
| B. | DFS |
| C. | Binary search |
| D. | Radix sort |
| Answer» B. DFS | |
| 71. |
Every Isomorphic graph must have ________ representation. |
| A. | cyclic |
| B. | adjacency list |
| C. | tree |
| D. | adjacency matrix |
| Answer» E. | |
| 72. |
A cycle on n vertices is isomorphic to its complement. What is the value of n? |
| A. | 5 |
| B. | 32 |
| C. | 17 |
| D. | 8 |
| Answer» B. 32 | |
| 73. |
An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if ____________ |
| A. | f(u) and f(v) are contained in G but not contained in H |
| B. | f(u) and f(v) are adjacent in H |
| C. | f(u * v) = f(u) + f(v) |
| D. | f(u) = f(u)² + f(v)² |
| Answer» C. f(u * v) = f(u) + f(v) | |
| 74. |
How many perfect matchings are there in a complete graph of 10 vertices? |
| A. | 60 |
| B. | 945 |
| C. | 756 |
| D. | 127 |
| Answer» C. 756 | |
| 75. |
A graph which has the same number of edges as its complement must have number of vertices congruent to ______ or _______ modulo 4(for integral values of number of edges). |
| A. | 6k, 6k-1 |
| B. | 4k, 4k+1 |
| C. | k, k+2 |
| D. | 2k+1, k |
| Answer» D. 2k+1, k | |
| 76. |
A graph G has the degree of each vertex is ≥ 3 say, deg(V) ≥ 3 ∀ V ∈ G such that 3|V| ≤ 2|E| and 3|R| ≤ 2|E|, then the graph is said to be ________ (R denotes region in the graph) |
| A. | Planner graph |
| B. | Polyhedral graph |
| C. | Homomorphic graph |
| D. | Isomorphic graph |
| Answer» C. Homomorphic graph | |
| 77. |
A complete n-node graph Kn is planar if and only if _____________ |
| A. | n ≥ 6 |
| B. | n² = n + 1 |
| C. | n ≤ 4 |
| D. | n + 3 |
| Answer» D. n + 3 | |
| 78. |
What is the grade of a planar graph consisting of 8 vertices and 15 edges? |
| A. | 30 |
| B. | 15 |
| C. | 45 |
| D. | 106 |
| Answer» B. 15 | |
| 79. |
A _______ is a graph with no homomorphism to any proper subgraph. |
| A. | poset |
| B. | core |
| C. | walk |
| D. | trail |
| Answer» C. walk | |
| 80. |
The 2ⁿ vertices of a graph G corresponds to all subsets of a set of size n, for n>=4. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. |
| A. | n+2 |
| B. | 3ⁿ/² |
| C. | n² |
| D. | 2ⁿ |
| Answer» C. n² | |
| 81. |
Let G be an arbitrary graph with v nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie down between _____ and _____ |
| A. | n-1 and n+1 |
| B. | v and k |
| C. | k+1 and v-k |
| D. | k-1 and v-1 |
| Answer» E. | |
| 82. |
The minimum number of edges in a connected cyclic graph on n vertices is _____________ |
| A. | n – 1 |
| B. | n |
| C. | 2n+3 |
| D. | n+1 |
| Answer» C. 2n+3 | |
| 83. |
The maximum number of edges in a 8-node undirected graph without self loops is ____________ |
| A. | 45 |
| B. | 61 |
| C. | 28 |
| D. | 17 |
| Answer» D. 17 | |
| 84. |
Any subset of edges that connects all the vertices and has minimum total weight, if all the edge weights of an undirected graph are positive is called _______ |
| A. | subgraph |
| B. | tree |
| C. | hamiltonian cycle |
| D. | grid |
| Answer» C. hamiltonian cycle | |
| 85. |
G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is ______ |
| A. | Complete bipartite graph |
| B. | Hamiltonian cycle |
| C. | Regular graph |
| D. | Euler graph |
| Answer» E. | |
| 86. |
A bridge can not be a part of _______ |
| A. | a simple cycle |
| B. | a tree |
| C. | a clique with size ≥ 3 whose every edge is a bridge |
| D. | a graph which contains cycles |
| Answer» B. a tree | |
| 87. |
______ is the maximum number of edges in an acyclic undirected graph with k vertices. |
| A. | k-1 |
| B. | k² |
| C. | 2k+3 |
| D. | k³+4 |
| Answer» B. k² | |
| 88. |
Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50. |
| A. | 98 |
| B. | 13 |
| C. | 6 |
| D. | 34 |
| Answer» D. 34 | |
| 89. |
What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6? |
| A. | 11 |
| B. | 14 |
| C. | 18 |
| D. | 19 |
| Answer» D. 19 | |
| 90. |
In a finite graph the number of vertices of odd degree is always ______ |
| A. | even |
| B. | odd |
| C. | even or odd |
| D. | infinite |
| Answer» B. odd | |
| 91. |
The graph representing universal relation is called _______ |
| A. | complete digraph |
| B. | partial digraph |
| C. | empty graph |
| D. | partial subgraph |
| Answer» B. partial digraph | |
| 92. |
What is a complete digraph? |
| A. | connection of nodes without containing any cycle |
| B. | connecting nodes to make at least three complete cycles |
| C. | start node and end node in a graph are same having a cycle |
| D. | connection of every node with every other node including itself in a digraph |
| Answer» E. | |
| 93. |
A directed graph or digraph can have directed cycle in which ______ |
| A. | starting node and ending node are different |
| B. | starting node and ending node are same |
| C. | minimum four vertices can be there |
| D. | ending node does not exist |
| Answer» C. minimum four vertices can be there | |
| 94. |
The graph given below is an example of _________ |
| A. | non-lattice poset |
| B. | semilattice |
| C. | partial lattice |
| D. | bounded lattice |
| Answer» B. semilattice | |
| 95. |
Let, D =
|
| A. | A’ ⊂ A and R’ = R ∩ (A’ x A’) |
| B. | A’ ⊂ A and R ⊂ R’ ∩ (A’ x A’) |
| C. | R’ = R ∩ (A’ x A’) |
| D. | A’ ⊆ A and R ⊆ R’ ∩ (A’ x A’) |
| Answer» B. A’ ⊂ A and R ⊂ R’ ∩ (A’ x A’) | |
| 96. |
The graph is the smallest non-modular lattice N₅. A lattice is _______ if and only if it does not have a _______ isomorphic to N₅. |
| A. | non-modular, complete lattice |
| B. | moduler, semilattice |
| C. | non-modular, sublattice |
| D. | modular, sublattice |
| Answer» E. | |
| 97. |
A simple graph can have _______ |
| A. | multiple edges |
| B. | self loops |
| C. | parallel edges |
| D. | no multiple edges, self-loops and parallel edges |
| Answer» E. | |
| 98. |
Degree of a graph with 12 vertices is _______ |
| A. | 25 |
| B. | 56 |
| C. | 24 |
| D. | 212 |
| Answer» D. 212 | |
| 99. |
Disconnected components can be created in case of ___________ |
| A. | undirected graphs |
| B. | partial subgraphs |
| C. | disconnected graphs |
| D. | complete graphs |
| Answer» D. complete graphs | |