Search results for graph / GATE Overflow for GATE CSE

60 votes

10 answers

1

GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$

How many perfect matching are there in a complete graph of $6$ vertices?$15$$24$$30$$60$

Kathleen

50.5k views

Kathleen asked Sep 16, 2014

113 votes

9 answers

2

GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$

Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...

gatecse

35.1k views

gatecse asked Sep 12, 2014

78 votes

12 answers

3

GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$

The number of distinct simple graphs with up to three nodes is$15$$10$$7$$9$

Kathleen

34.9k views

Kathleen asked Oct 4, 2014

31 votes

6 answers

4

GATE CSE 2008 | Question: 19
The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is: $\text{MNOPQR}$ $\text{NQMPOR}$ $\text{QMNPRO}$ $\text{QMNPOR}$

The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is:$\text{MNOPQR}$...

Kathleen

35.8k views

Kathleen asked Sep 11, 2014

101 votes

10 answers

5

GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.

Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $...

go_editor

26.9k views

go_editor asked Sep 28, 2014

59 votes

7 answers

6

GATE CSE 2006 | Question: 12
To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is: Queue Stack Heap B-Tree

To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:QueueStackHeapB-Tree

Rucha Shelke

31.7k views

Rucha Shelke asked Sep 16, 2014

66 votes

9 answers

7

GATE CSE 2012 | Question: 40
Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices $S$ and $T$. Which one will be reported by Dijkstra's shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex $v$ is updated only ... a strictly shorter path to $v$ is discovered. $\text{SDT}$ $\text{SBDT}$ $\text{SACDT}$ $\text{SACET}$

Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices $S$ and $T$. Which one will be reported by Dijkstra’s shortest...

gatecse

26.9k views

gatecse asked Sep 26, 2014

63 votes

11 answers

8

GATE CSE 2008 | Question: 45
Dijkstra's single source shortest path algorithm when run from vertex $a$ in the above graph, computes the correct shortest path distance to only vertex $a$ only vertices $a, e, f, g, h$ only vertices $a, b, c, d$ all the vertices

Dijkstra's single source shortest path algorithm when run from vertex $a$ in the above graph, computes the correct shortest path distance toonly vertex $a$only vertices $...

Kathleen

27.7k views

Kathleen asked Sep 12, 2014

67 votes

4 answers

9

GATE CSE 2014 Set 3 | Question: 34
Consider the basic block given below. a = b + c c = a + d d = b + c e = d - b a = e + b The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are $6$ and $6$ $8$ and $10$ $9$ and $12$ $4$ and $4$

Consider the basic block given below. a = b + c c = a + d d = b + c e = d - b a = e + b The minimum number of nodes and edges present in the DAG representation of the abo...

go_editor

35.3k views

go_editor asked Sep 28, 2014

61 votes

5 answers

10

GATE CSE 2016 Set 1 | Question: 11
Consider the following directed graph: The number of different topological orderings of the vertices of the graph is _____________.

Consider the following directed graph:The number of different topological orderings of the vertices of the graph is _____________.

Sandeep Singh

28.6k views

Sandeep Singh asked Feb 12, 2016

39 votes

9 answers

11

GATE CSE 2014 Set 2 | Question: 3
The maximum number of edges in a bipartite graph on $12$ vertices is____

The maximum number of edges in a bipartite graph on $12$ vertices is____

go_editor

27.2k views

go_editor asked Sep 28, 2014

65 votes

9 answers

12

GATE CSE 2016 Set 1 | Question: 38
Consider the weighted undirected graph with $4$ vertices, where the weight of edge $\{i,j\}$ is given by the entry $W_{ij}$ in the matrix $W$ ... integer value of $x$, for which at least one shortest path between some pair of vertices will contain the edge with weight $x$ is ___________.

Consider the weighted undirected graph with $4$ vertices, where the weight of edge $\{i,j\}$ is given by the entry $W_{ij}$ in the matrix $W$. W=$\begin{bmatrix} 0&2 &8 &...

Sandeep Singh

24.1k views

Sandeep Singh asked Feb 12, 2016

33 votes

14 answers

13

GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$

Let $G$ be an undirected complete graph on $n$ vertices, where $n 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to$n!$$(n-1)!$$1$$\frac{(n-1)!}{2}...

Arjun

21.4k views

Arjun asked Feb 7, 2019

38 votes

5 answers

14

GATE CSE 2020 | Question: 31
Let $G = (V, E)$ be a weighted undirected graph and let $T$ be a Minimum Spanning Tree (MST) of $G$ maintained using adjacency lists. Suppose a new weighed edge $(u, v) \in V \times V$ is added to $G$. The worst case time complexity of determining if $T$ is still an MST ... $\Theta (\mid E \mid \mid V \mid) \\$ $\Theta(E \mid \log \mid V \mid) \\$ $\Theta( \mid V \mid)$

Let $G = (V, E)$ be a weighted undirected graph and let $T$ be a Minimum Spanning Tree (MST) of $G$ maintained using adjacency lists. Suppose a new weighed edge $(u, v) ...

Arjun

19.1k views

Arjun asked Feb 12, 2020

33 votes

9 answers

15

GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

makhdoom ghaya

24.7k views

makhdoom ghaya asked Feb 13, 2015

90 votes

12 answers

16

GATE CSE 2006 | Question: 48
Let $T$ be a depth first search tree in an undirected graph $G$. Vertices $u$ and $ν$ are leaves of this tree $T$. The degrees of both $u$ and $ν$ in $G$ are at least $2$ ... exist a cycle in $G$ containing $u$ and $ν$ There must exist a cycle in $G$ containing $u$ and all its neighbours in $G$

Let $T$ be a depth first search tree in an undirected graph $G$. Vertices $u$ and $ν$ are leaves of this tree $T$. The degrees of both $u$ and $ν$ in $G$ are at least $...

Rucha Shelke

21.2k views

Rucha Shelke asked Sep 26, 2014

89 votes

6 answers

17

GATE CSE 2006 | Question: 72
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$

The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets...

go_editor

17.9k views

go_editor asked Apr 24, 2016

65 votes

12 answers

18

GATE IT 2005 | Question: 14
In a depth-first traversal of a graph $G$ with $n$ vertices, $k$ edges are marked as tree edges. The number of connected components in $G$ is $k$ $k+1$ $n-k-1$ $n-k$

In a depth-first traversal of a graph $G$ with $n$ vertices, $k$ edges are marked as tree edges. The number of connected components in $G$ is$k$$k+1$$n-k-1$$n-k$

Ishrat Jahan

17.9k views

Ishrat Jahan asked Nov 3, 2014

86 votes

5 answers

19

GATE CSE 2003 | Question: 67
Let $G =(V,E)$ be an undirected graph with a subgraph $G_1 = (V_1, E_1)$. Weights are assigned to edges of $G$ as follows. $w(e) = \begin{cases} 0 \text{, if } e \in E_1 \\1 \text{, otherwise} \end{cases}$ A single-source shortest path ... edges in the shortest paths from $v_1$ to all vertices of $G$ $G_1$ is connected $V_1$ forms a clique in $G$ $G_1$ is a tree

Let $G =(V,E)$ be an undirected graph with a subgraph $G_1 = (V_1, E_1)$. Weights are assigned to edges of $G$ as follows.$$w(e) = \begin{cases} 0 \text{, if } e \in E_...

Kathleen

20.2k views

Kathleen asked Sep 17, 2014

39 votes

6 answers

20

GATE CSE 2020 | Question: 40
Let $G = (V,E)$ be a directed, weighted graph with weight function $w: E \rightarrow \mathbb{R}$. For some function $f: V \rightarrow \mathbb{R}$, for each edge$(u,v)\in E$, define ${w}'(u,v)$ as $w(u,v)+f(u)-f(v)$. Which one of the ... from $s$ to $u$ in the graph obtained by adding a new vertex $s$ to $G$ and edges of zero weight from $s$ to every vertex of $G$

Let $G = (V,E)$ be a directed, weighted graph with weight function $w: E \rightarrow \mathbb{R}$. For some function $f: V \rightarrow \mathbb{R}$, for each edge$(u,v)\in ...

Arjun

18.2k views

Arjun asked Feb 12, 2020

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