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Recent questions tagged gb2019ds2
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GATEBOOK2019DS21
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? $7, 5, 5, 3, 3, 2, 2, 2$ $6, 6, 6, 6, 3, 3, 2, 2, 1, 1$ $8, 7, 6, 4, 4, 3, 2, 2, 2$ $8, 7, 6, 6, 4, 4, 2, 2, 2$ II and III III and IV IV only I and IV
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Oct 16, 2018
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gb2019ds2
graphtheory
degreeofgraph
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GATEBOOK2019DS22
Let $G$ be an undirected labelled graph with $8$ vertices. Every vertex in $G$ is connected with every other vertex except one vertex which is not connected with any of the vertex. Which of the following represents number of distinct cycles of length $5$ in $G$: 252 490 504 662
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Oct 16, 2018
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Programming
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151
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gb2019ds2
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GATEBOOK2019DS23
A quinpartite graph is a graph whose vertices can be partitioned into five groups such that no two vertices in same group are connected via some edge. The maximum number of edges in a quinpartite graph with $10$ vertices, where cardinalities of those five sets are given as $\{2,3,2,1,2\},$ is: $16$ $20$ $26$ $39$
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Oct 16, 2018
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Programming
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13.8k
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167
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gb2019ds2
graphtheory
graphconnectivity
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GATEBOOK2019DS24
Consider a weighted undirected graph with positive integer edge weights and let there be edges or at least one path between each of the vertices u,v and k. It is known that the shortest path from the source vertex s to u has weight $79$, shortest path from s to k has weight $31$ and the ... $\text{weight } (u, k) \le 48$ $\text{weight }(u, v) \ge 24$
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Oct 16, 2018
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13.8k
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58
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gb2019ds2
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1
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GATEBOOK2019DS25
Consider following statements about tripartite graph, i.e. TPG, which contains three subsets of vertices of graph as A,B and C: Minimum number of edges in a cycle in a TPG which passes through all three subsets of vertices is $6$ ... . Which of the above statements are true: (i) only (iii) only (ii) and (iii) only (i) and (ii) only
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Oct 16, 2018
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66
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gb2019ds2
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GATEBOOK2019DS26
Let $\alpha(G)$ be the size of the largest independent set in a graph $G$, and $\chi(G)$ the chromatic number of $G$. Which of the following statements about a graph is true? $\alpha(G)*\chi(G) \ge G$ $\alpha(G) > \chi(G)$ $\alpha(G) < \chi(G)$ $\alpha(G)*\chi(G) \le G$
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Oct 16, 2018
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75
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gb2019ds2
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GATEBOOK2019DS27
In a binary tree with $n$ nodes, every nonleaf node has an even number of descendants. Every node is considered to be its own descendant. What is the number of nodes in a tree that has exactly one child? $0$ $1$ $\frac{(n  1)}{2}$ $n1$
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Oct 16, 2018
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13.8k
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197
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gb2019ds2
binarytree
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GATEBOOK2019DS28
Consider following four graphs each with five vertices whose edgesets are shown below: $\{(1,3),(2,4),(1,2),(2,3),(3,5),(4,5)\}$ $\{(1,2),(2,3),(3,4),(4,5),(2,4)\}$ $\{(2,3),(1,2),(1,5),(2,5),(1,3),(3,4)\}$ $\{(1,4),(3,5),(2,4),(4,5),(1,2),(2,3)\}$ Which of the above graphs are isomorphic to each other: (i), (ii) and (iii) (ii) and (iii) (i) and (iv) None of the above
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Oct 16, 2018
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73
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gb2019ds2
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0
answers
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GATEBOOK2019DS29
Consider following statements: Every simple graph has at least two vertices of the same degree. If u is a vertex of odd degree in a graph, then there exists a path from u to another vertex v of the graph where v also has odd degree. If there are exactly two ... the graph. Which of the above statements are not true? (i) and (ii) only (iii) only (ii) only None of the above
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Oct 16, 2018
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44
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gb2019ds2
0
votes
1
answer
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GATEBOOK2019DS210
For which of the following scenarios does there exist a simple graph $G = (V, E)$ satisfying the specified conditions? It has $3$ components $20$ vertices and $16$ edges. It has $10$ vertices, $38$ edges, and more than one component. It has $7$ vertices, $10$ edges, and more than two components. It is connected and has $10$ edges $5$ vertices and fewer than $6$ cycles.
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Oct 16, 2018
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GATEBOOK
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13.8k
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50
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gb2019ds2
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votes
1
answer
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GATEBOOK2019DS211
The number of simple digraphs with $\mid V \mid = 3$ is: $8$ $27$ $64$ $256$
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Oct 16, 2018
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115
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gb2019ds2
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GATEBOOK2019DS212
Let $T = (V, E)$ be a tree and let $d(v)$ be the degree of a vertex. Consider following statements: $\sum_{v\in V}(2  d(v)) = 2$ If $T$ has a vertex of degree $m \ge 2$, then it has at least m vertices of degree $1$. $\sum_{v\in V}(k  d(v)) = k$, ... Which of the above statements is/are true? (i) only (i), (ii) only (ii) and (iii) only (i), (ii) and (iii) only
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Oct 16, 2018
in
Programming
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GATEBOOK
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13.8k
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66
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gb2019ds2
+3
votes
1
answer
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GATEBOOK2019DS213
For which of the following scenarios does there exist a Binary tree satisfying the specified conditions? A binary tree with $35$ leaves and height $100$. A full binary tree with $21$ leaves and height $21$. A binary tree with $33$ leaves and height $5$. A rooted tree of height $5$ where every internal vertex has $3$ children and there are $365$ vertices.
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Oct 16, 2018
in
Programming
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GATEBOOK
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13.8k
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82
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gb2019ds2
0
votes
2
answers
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GATEBOOK2019DS214
For each of the following graphs, the number of spanning trees are A, B and C, respectively. \The value of $A*B+C$ is: $16$ $32$ $48$ $64$
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Oct 16, 2018
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GATEBOOK
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13.8k
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52
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gb2019ds2
0
votes
1
answer
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GATEBOOK2019DS215
The chromatic number of the following graph is: \ $2$ $3$ $4$ $5$
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Oct 16, 2018
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Programming
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GATEBOOK
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13.8k
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66
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gb2019ds2
+1
vote
1
answer
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GATEBOOK2019DS216
Consider the weighted undirected graph shown below: The weight of the minimum spanning tree of the above graph is: $25$ $28$ $30$ $33$
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Oct 16, 2018
in
Programming
by
GATEBOOK
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13.8k
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50
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gb2019ds2
+2
votes
1
answer
17
GATEBOOK2019DS217
The line graph $L(G)$ of a graph $G(V,E)$ is a graph whose vertices are in $11$ correspondence with the edges of $G$. Two vertices of $L(G)$ being adjacent if the corresponding edges of $G$ are adjacent. Consider following graphs: Consider following statements: L(A) is ... graphs are true? (i) and (iii) only (ii) and (iii) only (ii) and (iv) only (ii), (iii) and (iv) only
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Oct 16, 2018
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GATEBOOK
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13.8k
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62
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gb2019ds2
+2
votes
1
answer
18
GATEBOOK2019DS218
Consider following statements about Cycle graph, Complete Bipartite graph and Complete graph. Cycle graph $C_n$ is subgraph of a complete graph $K_n$. $K_{n,n}$ is a subgraph of $K_m$ if $m\le 2n$. $C_n$ a subgraph of $K_{n,n}$ if $n$ is even. Which of the above statements is/are TRUE? (i) and (iii) only (ii) and (iii) only (i) only (iii) only
asked
Oct 16, 2018
in
Programming
by
GATEBOOK
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(
13.8k
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98
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gb2019ds2
graphconnectivity
+2
votes
1
answer
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GATEBOOK2019DS219
Consider the following graph ? Let number of shortest paths from node $a$ to node $j$ is represented by $A$, number of shortest paths from node $e$ to node $b$ is represented by $B$ and number of shortest paths from node $b$ to node $f$ is represented by $C$. Then the value of the expression: $A^B+B^C+C^A$ is: $13$ $21$ $57$ $64$
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Oct 16, 2018
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Programming
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GATEBOOK
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13.8k
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89
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gb2019ds2
0
votes
1
answer
20
GATEBOOK2019DS220
Consider the graph shown below: Cardinality of the largest maximum independent set of the above graph is __________?
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Oct 16, 2018
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Programming
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86
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gb2019ds2
numericalanswers
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