Search results for graph / GATE Overflow for GATE CSE

33 votes

5 answers

21

GATE CSE 1995 | Question: 1.25
The minimum number of edges in a connected cyclic graph on $n$ vertices is: $n-1$ $n$ $n+1$ None of the above

The minimum number of edges in a connected cyclic graph on $n$ vertices is:$n-1$$n$$n+1$None of the above

Kathleen

21.3k views

Kathleen asked Oct 8, 2014

51 votes

10 answers

22

GATE CSE 2015 Set 1 | Question: 45
Let $G = (V, E)$ be a simple undirected graph, and $s$ be a particular vertex in it called the source. For $x \in V$, let $d(x)$ denote the shortest distance in $G$ from $s$ to $x$. A breadth first search (BFS) is performed starting at $s$. Let $T$ be the ... that is not in $T$, then which one of the following CANNOT be the value of $d(u) - d(v)$? $-1$ $0$ $1$ $2$

Let $G = (V, E)$ be a simple undirected graph, and $s$ be a particular vertex in it called the source. For $x \in V$, let $d(x)$ denote the shortest distance in $G$ from ...

makhdoom ghaya

18.6k views

makhdoom ghaya asked Feb 13, 2015

76 votes

5 answers

23

GATE CSE 2007 | Question: 23
Which of the following graphs has an Eulerian circuit? Any $k$-regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above

Which of the following graphs has an Eulerian circuit?Any $k$-regular graph where $k$ is an even number.A complete graph on $90$ vertices.The complement of a cycle on $25...

Kathleen

25.6k views

Kathleen asked Sep 21, 2014

0 votes

3 answers

24

NIELIT 2017 July Scientist B (IT) - Section B: 2
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list ... Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.

Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph?In adjacency list representation, space is saved f...

admin

18.0k views

admin asked Mar 30, 2020

47 votes

7 answers

25

GATE CSE 2018 | Question: 30
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ ... $\mid i-j \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II

Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements.No...

gatecse

27.6k views

gatecse asked Feb 14, 2018

63 votes

5 answers

26

GATE CSE 2018 | Question: 43
Let $G$ be a graph with $100!$ vertices, with each vertex labelled by a distinct permutation of the numbers $1, 2,\ldots, 100.$ There is an edge between vertices $u$ and $v$ if and only if the label of $u$ can be obtained by swapping two adjacent ... denote the degree of a vertex in $G$, and $z$ denote the number of connected components in $G$. Then, $y+10z=$ ______.

Let $G$ be a graph with $100!$ vertices, with each vertex labelled by a distinct permutation of the numbers $1, 2,\ldots, 100.$ There is an edge between vertices $u$ and ...

gatecse

20.0k views

gatecse asked Feb 14, 2018

40 votes

6 answers

27

GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II

Let $G$ be any connected, weighted, undirected graph.$G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight.$G$ has a unique minimum spanning...

Arjun

20.7k views

Arjun asked Feb 7, 2019

28 votes

6 answers

28

GATE CSE 2020 | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______

Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is...

Arjun

13.8k views

Arjun asked Feb 12, 2020

49 votes

7 answers

29

GATE CSE 2009 | Question: 13
Which of the following statement(s) is/are correct regarding Bellman-Ford shortest path algorithm? P: Always finds a negative weighted cycle, if one exists. Q: Finds whether any negative weighted cycle is reachable from the source. $P$ only $Q$ only Both $P$ and $Q$ Neither $P$ nor $Q$

Which of the following statement(s) is/are correct regarding Bellman-Ford shortest path algorithm?P: Always finds a negative weighted cycle, if one exists.Q: Finds whethe...

Kathleen

16.9k views

Kathleen asked Sep 22, 2014

86 votes

8 answers

30

GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$

How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...

Kathleen

14.6k views

Kathleen asked Sep 18, 2014

58 votes

7 answers

31

GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$

What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$

Ishrat Jahan

59.2k views

Ishrat Jahan asked Oct 27, 2014

52 votes

10 answers

32

GATE CSE 2011 | Question: 54
An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$ are connected if and only if $ 0 < \mid i-j\mid \leq 2$. Each edge $(v_i,v_j)$ is assigned a weight $i+j$. A sample graph with $n=4$ is shown below. ... spanning tree (MST) of such a graph with $n$ nodes? $\frac{1}{12} (11n^2 - 5 n)$ $n^2-n+1$ $6n-11$ $2n+1$

An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$ are connected if and only if $ 0 < \mid i-j\mid \leq 2$. Each ...

go_editor

17.4k views

go_editor asked Sep 29, 2014

20 votes

6 answers

33

GATE CSE 2021 Set 2 | Question: 1
Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a ... are true $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false

Let $G$ be a connected undirected weighted graph. Consider the following two statements.$S_1$: There exists a minimum weight edge in $G$ which is present in every minimum...

Arjun

12.0k views

Arjun asked Feb 18, 2021

94 votes

4 answers

34

GATE CSE 2016 Set 2 | Question: 41
In an adjacency list representation of an undirected simple graph $G=(V, E)$, each edge $(u, v)$ has two adjacency list entries: $[v]$ in the adjacency list of $u$, and $[u]$ in the adjacency list of $v$. These are called twins of each other. A twin pointer ... $\Theta\left(n+m\right)$ $\Theta\left(m^{2}\right)$ $\Theta\left(n^{4}\right)$

In an adjacency list representation of an undirected simple graph $G=(V, E)$, each edge $(u, v)$ has two adjacency list entries: $[v]$ in the adjacency list of $u$, and $...

Akash Kanase

19.8k views

Akash Kanase asked Feb 12, 2016

73 votes

6 answers

35

GATE IT 2007 | Question: 25
What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ? $1$ $2$ $3$ $n$

What is the largest integer $m$ such that every simple connected graph with $n$ vertices and $n$ edges contains at least $m$ different spanning trees ?$1$$2$$3$$n$

Ishrat Jahan

21.7k views

Ishrat Jahan asked Oct 29, 2014

65 votes

9 answers

36

GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$

A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...

Kathleen

15.9k views

Kathleen asked Sep 17, 2014

59 votes

8 answers

37

GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if ... planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only

The line graph $L(G)$ of a simple graph $G$ is defined as follows:There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$.For any two edges $e$ and $e'$ in ...

Arjun

19.3k views

Arjun asked Sep 24, 2014

37 votes

3 answers

38

GATE CSE 2004 | Question: 44
Suppose we run Dijkstra’s single source shortest path algorithm on the following edge-weighted directed graph with vertex $P$ as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized? $P,Q,R,S,T,U$ $P,Q,R,U,S,T$ $P,Q,R,U,T,S$ $P,Q,T,R,U,S$

Suppose we run Dijkstra’s single source shortest path algorithm on the following edge-weighted directed graph with vertex $P$ as the source.In what order do the nodes g...

Kathleen

15.8k views

Kathleen asked Sep 18, 2014

77 votes

6 answers

39

GATE CSE 2008 | Question: 42
$G$ is a graph on $n$ vertices and $2n-2$ edges. The edges of $G$ can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for $G$? For every subset of $k$ vertices, the induced subgraph has at ... least $2$ edge-disjoint paths between every pair of vertices. There are at least $2$ vertex-disjoint paths between every pair of vertices.

$G$ is a graph on $n$ vertices and $2n-2$ edges. The edges of $G$ can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for $G$?For...

Akshay Jindal

23.8k views

Akshay Jindal asked Sep 27, 2014

65 votes

5 answers

40

GATE CSE 2003 | Question: 8, ISRO2009-53
Let $\text{G}$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $\text{G}$, the number of components in the resultant graph must necessarily lie down between $k$ and $n$ $k-1$ and $k+1$ $k-1$ and $n-1$ $k+1$ and $n-k$

Let $\text{G}$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $\text{G}$, the number of components in the resultant graph must neces...

Kathleen

15.5k views

Kathleen asked Sep 16, 2014

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