Search results for graph-theory / GATE Overflow for GATE CSE

2 votes

2 answers

41

GATE CSE 2024 | Set 2 | Question: 7
Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements is always TRUE? $\text{G}$ is a cycle $\text{G}$ is a perfect matching $\text{G}$ is a complete graph There is no such graph $\text{G}$

Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements i...

Arjun

2.9k views

Arjun asked Feb 16

46 votes

6 answers

42

GATE CSE 2002 | Question: 1.4
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is $2$ $3$ $4$ $n-2 \left \lfloor \frac{n}{2} \right \rfloor+2$

The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is$2$$3$$4$$n-2 \lef...

Kathleen

11.2k views

Kathleen asked Sep 15, 2014

1 votes

3 answers

43

GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.

Arjun

1.9k views

Arjun asked Feb 16

40 votes

7 answers

44

GATE CSE 2010 | Question: 28
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? $7, 6, 5, 4, 4, 3, 2, 1$ $6, 6, 6, 6, 3, 3, 2, 2$ $7, 6, 6, 4, 4, 3, 2, 2$ $8, 7, 7, 6, 4, 2, 1, 1$ I and II III and IV IV only II and IV

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...

gatecse

18.6k views

gatecse asked Sep 21, 2014

43 votes

8 answers

45

GATE CSE 2006 | Question: 73
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 number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$

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 set...

go_editor

8.8k views

go_editor asked Apr 24, 2016

14 votes

2 answers

46

GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)

The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are $\text{TRUE}?$The chromatic number of the graph is $3....

Arjun

7.6k views

Arjun asked Feb 15, 2022

35 votes

6 answers

47

GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$

Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as:$$\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortes...

Arjun

10.0k views

Arjun asked Feb 18, 2021

13 votes

1 answer

48

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, a vertex of degree 5 , a vertex of degree 6 and ... of degree 7. Which of the following can be the degree of the last vertex? (Select all that are possible) 0 3 4 8

Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, ...

GO Classes

660 views

GO Classes asked Feb 5

0 votes

1 answer

49

ISI kolkata MTech CS 2019
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths from $u$ to $v$ that do not contain the vertex $w$.

Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths fro...

suvasish114

50 views

suvasish114 asked 6 days ago

0 votes

1 answer

50

Practice Material Question
If G is a connected graph with 6 vertices and maximum number of edges, then which of the following is true ? (a) Euler path exists, but Euler circuit does not exist in G. (b) Only Euler path exists in G. (c) Euler circuit does not exists in G (d) G is not traversable.

If G is a connected graph with 6 vertices and maximum number of edges, then which of the following is true ? (a) Euler path exists, but Euler circuit does not exist in G....

Akash Chakraborty

105 views

Akash Chakraborty asked Mar 30

0 votes

1 answer

51

Made Easy Mock Test 2

Rohit Chakraborty

270 views

Rohit Chakraborty asked Jan 11

0 votes

1 answer

52

Made Easy Test Series 2024
Suppose we have a directed graph G = (V,E) with V= {1, 2, ..., n} and Eis presented as an adjacency list. For each vertex u in V, out(u) is a list such that (u, v) in {1, 2, ... k). For each u in V, we wish to compute a corresponding list in(u) =such that in E ... take to construct the lists in(u), u in V, from the lists out(u), u in V? T(n) =O(n+m) B. T(n)= O(n(m+n))

Suppose we have a directed graph G = (V,E) with V= {1, 2, ..., n} and Eis presented as an adjacency list. For each vertex u in V, out(u) is a list such that (u, v) in {1,...

Ray Tomlinson

542 views

Ray Tomlinson asked Aug 9, 2023

6 votes

1 answer

53

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$

A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ is a maximal set of vertices such that any two vertices in the s...

GO Classes

558 views

GO Classes asked Feb 5

0 votes

1 answer

54

GATE CSE 2024 | Set 1 | Question: 41
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic nu...

Arjun

2.0k views

Arjun asked Feb 16

4 votes

1 answer

55

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 46
Assume the following graph is a labeled graph i.e. every vertex has a unique label. In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors $\{R, G, B, W, Y, M\}$ such that no two adjacent vertices are assigned the same color?

Assume the following graph is a labeled graph i.e. every vertex has a unique label.In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors ...

GO Classes

645 views

GO Classes asked Jan 21

0 votes

1 answer

56

#algorithm
how many spanning trees are possible for complete graph of 4 vertices

how many spanning trees are possible for complete graph of 4 vertices

Amoljadhav

136 views

Amoljadhav asked Mar 1

28 votes

6 answers

57

GATE CSE 2015 Set 2 | Question: 28
A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ is A multiple of 4 Even Odd Congruent to 0 $mod$ 4, or, 1 $mod$ 4.

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $n$ vertices, $n$ isA multiple of 4EvenOddCongruent to 0 $mod$ 4...

go_editor

13.7k views

go_editor asked Feb 12, 2015

3 votes

1 answer

58

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 63
For an undirected graph $G$, let $\overline{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\overline{G}$ if and only if it is not an edge in $G$ ). Consider the following ... is equivalent to (iii) and (v). (i) is equivalent to (ii) and (iv). (i) is equivalent to (ii) and (v)

For an undirected graph $G$, let $\overline{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\overline{G}$ if and only if ...

GO Classes

449 views

GO Classes asked Jan 28

3 votes

1 answer

59

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 11
The figure above shows an undirected graph with six vertices. Enough edges are to be deleted from the graph in order to leave a spanning tree, which is a connected subgraph having the same six vertices and no cycles. How many edges must be deleted?

The figure above shows an undirected graph with six vertices. Enough edges are to be deleted from the graph in order to leave a spanning tree, which is a connected subgra...

GO Classes

450 views

GO Classes asked Jan 13

57 votes

11 answers

60

GATE CSE 2014 Set 3 | Question: 51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$

If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have?$\left\lfloor\frac {n}{k}\right\rfloor$$\left\lceil \frac{n}{k} \right\r...

go_editor

18.4k views

go_editor asked Sep 28, 2014

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