Recent questions tagged graph-theory

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1

NIELIT 2017 DEC Scientist B - Section B: 23
Let $G$ be a complete undirected graph on $8$ vertices. If vertices of $G$ are labelled, then the number of distinct cycles of length $5$ in $G$ is equal to: $15$ $30$ $56$ $60$

Let $G$ be a complete undirected graph on $8$ vertices. If vertices of $G$ are labelled, then the number of distinct cycles of length $5$ in $G$ is equal to: $15$ $30$ $56$ $60$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 97 views

0 votes

3 answers

2

NIELIT 2017 DEC Scientist B - Section B: 52
Let $G$ be a simple undirected graph on $n=3x$ vertices $(x \geq 1)$ with chromatic number $3$, then maximum number of edges in $G$ is $n(n-1)/2$ $n^{n-2}$ $nx$ $n$

Let $G$ be a simple undirected graph on $n=3x$ vertices $(x \geq 1)$ with chromatic number $3$, then maximum number of edges in $G$ is $n(n-1)/2$ $n^{n-2}$ $nx$ $n$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 203 views

0 votes

1 answer

3

UGCNET-Jan2017-II: 5
Consider a Hamiltonian Graph $G$ with no loops or parallel edges and with $\left | V\left ( G \right ) \right |= n\geq 3$. The which of the following is true? $\text{deg}\left ( v \right )\geq \frac{n}{2}$ for each vertex $v\\$ ... $v$ and $w$ are not connected by an edge All of the above

Consider a Hamiltonian Graph $G$ with no loops or parallel edges and with $\left | V\left ( G \right ) \right |= n\geq 3$. The which of the following is true? $\text{deg}\left ( v \right )\geq \frac{n}{2}$ for each vertex $v\\$ ... $v$ and $w$ are not connected by an edge All of the above

asked Mar 24 in Graph Theory jothee 85 views

6 votes

3 answers

4

GATE2020-CS-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 _______

asked Feb 12 in Graph Theory Arjun 1.7k views

0 votes

3 answers

5

TIFR2020-B-11
Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$

Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$

asked Feb 11 in Graph Theory Lakshman Patel RJIT 140 views

2 votes

1 answer

6

CMI2019-A-7
An interschool basketball tournament is being held at the Olympic sports complex. There are multiple basketball courts. Matches are scheduled in parallel, with staggered timings, to ensure that spectators always have some match or other available to watch. Each match ... solve? Find a minimal colouring. Find a minimal spanning tree. Find a minimal cut. Find a minimal vertex cover.

An interschool basketball tournament is being held at the Olympic sports complex. There are multiple basketball courts. Matches are scheduled in parallel, with staggered timings, to ensure that spectators always have some match or other available to watch. Each match requires a ... to solve? Find a minimal colouring. Find a minimal spanning tree. Find a minimal cut. Find a minimal vertex cover.

asked Sep 13, 2019 in Graph Theory gatecse 158 views

4 votes

2 answers

7

CMI2018-A-4
Let $G=(V, E)$ be an undirected simple graph, and $s$ be a designated vertex in $G.$ For each $v\in V,$ let $d(v)$ be the length of a shortest path between $s$ and $v.$ For an edge $(u,v)$ in $G,$ what can not be the value of $d(u)-d(v)?$ $2$ $-1$ $0$ $1$

Let $G=(V, E)$ be an undirected simple graph, and $s$ be a designated vertex in $G.$ For each $v\in V,$ let $d(v)$ be the length of a shortest path between $s$ and $v.$ For an edge $(u,v)$ in $G,$ what can not be the value of $d(u)-d(v)?$ $2$ $-1$ $0$ $1$

asked Sep 13, 2019 in Graph Theory gatecse 146 views

0 votes

1 answer

8

CMI2018-A-9
Your college has sent a contingent to take part in a cultural festival at a neighbouring institution. Several team events are part of the programme. Each event takes place through the day with many elimination rounds. Your contingent is multi-talented ... : Find a maximum length simple cycle Find a maximum size independent set Find a maximum matching Find a maximal connected component

Your college has sent a contingent to take part in a cultural festival at a neighbouring institution. Several team events are part of the programme. Each event takes place through the day with many elimination rounds. Your contingent is multi-talented and each ... is: Find a maximum length simple cycle Find a maximum size independent set Find a maximum matching Find a maximal connected component

asked Sep 13, 2019 in Graph Theory gatecse 106 views

1 vote

1 answer

9

CMI2018-B-3
Let $G$ be a simple graph on $n$ vertices. Prove that if $G$ has more than $\binom{n-1}{2}$ edges then $G$ is connected. For every $n>2$, find a graph $G_{n}$ which has exactly $n$ vertices and $\binom{n-1}{2}$ edges, and is not connected.

Let $G$ be a simple graph on $n$ vertices. Prove that if $G$ has more than $\binom{n-1}{2}$ edges then $G$ is connected. For every $n>2$, find a graph $G_{n}$ which has exactly $n$ vertices and $\binom{n-1}{2}$ edges, and is not connected.

asked Sep 13, 2019 in Graph Theory gatecse 99 views

1 vote

0 answers

10

CMI2018-B-5
Let $G=(V,E)$ be an undirected graph and $V=\{1,2,\cdots,n\}.$ The input graph is given to you by a $0-1$ matrix $A$ of size $n\times n$ as follows. For any $1\leq i,j\leq n,$ the entry $A[i,j]=1$ if and only if ... any two vertices are connected to each other by paths. Give a simple algorithm to find the number of connected components in $G.$ Analyze the time taken by your procedure.

Let $G=(V,E)$ be an undirected graph and $V=\{1,2,\cdots,n\}.$ The input graph is given to you by a $0-1$ matrix $A$ of size $n\times n$ as follows. For any $1\leq i,j\leq n,$ the entry $A[i,j]=1$ ... which any two vertices are connected to each other by paths. Give a simple algorithm to find the number of connected components in $G.$ Analyze the time taken by your procedure.

asked Sep 13, 2019 in Graph Theory gatecse 69 views

3 votes

2 answers

11

UGCNET-June-2019-II: 5
For which values of $m$ and $n$ does the complete bipartite graph $k_{m,n}$ have a Hamiltonian circuit ? $m\neq n,\ \ m,n \geq 2$ $m\neq n,\ \ m,n \geq 3$ $m=n,\ \ m,n \geq 2$ $m= n,\ \ m,n \geq 3$

For which values of $m$ and $n$ does the complete bipartite graph $k_{m,n}$ have a Hamiltonian circuit ? $m\neq n,\ \ m,n \geq 2$ $m\neq n,\ \ m,n \geq 3$ $m=n,\ \ m,n \geq 2$ $m= n,\ \ m,n \geq 3$

asked Jul 2, 2019 in Graph Theory Arjun 529 views

0 votes

1 answer

12

Doubt on Bipartite Graph
What is T.C. to find maximum number of edges to be added to a tree so that it stays as a bipartite graph? Now my question is, why do we need to add edges to make a tree bipartite? A tree is already bipartite graph. Right?? Again how do we add edges in it?? Is BFS or DFS do any improvement in such a tree?? How to think such a question??

What is T.C. to find maximum number of edges to be added to a tree so that it stays as a bipartite graph? Now my question is, why do we need to add edges to make a tree bipartite? A tree is already bipartite graph. Right?? Again how do we add edges in it?? Is BFS or DFS do any improvement in such a tree?? How to think such a question??

asked Jun 2, 2019 in Algorithms srestha 135 views

2 votes

1 answer

13

ACE ACADEMY BOOKLET
Which of the following is $\textbf{not}$ TRUE? (a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Hamiltonian cycle exists for all n. (b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Hamiltonian cycle exists $\Leftrightarrow$ ... Hamiltonian cycle exits for all $n$ (d) In a wheel graph $W_n$ ($n \geq 4$), Hamiltonian cycle exits $\Leftrightarrow$ $n$ is even.

Which of the following is $\textbf{not}$ TRUE? (a) In a complete graph $K_n$ ($n$ $\geq$ $3$), Hamiltonian cycle exists for all n. (b) In a complete bipartite graph $K_{m,n}$ (m $\geq$ 2 and n $\geq$2), Hamiltonian cycle exists $\Leftrightarrow$ $m$ $=$ $n$ ... $n$ (d) In a wheel graph $W_n$ ($n \geq 4$), Hamiltonian cycle exits $\Leftrightarrow$ $n$ is even.

asked May 26, 2019 in Graph Theory `JEET 138 views

1 vote

2 answers

14

#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edge-disjoint Hamiltonian cycles in $K_7$ is $3$ (b) If $G$ is a simple graph with $6$ vertices and the degree of each vertex is at least $3$, then the Hamiltonian cycle exists in ... simple graph with $5$ vertices and $7$ edges, then the Hamiltonian cycle exists in $G$ Please help me understand all the options.

Which of the following is not true? (a) Number of edge-disjoint Hamiltonian cycles in $K_7$ is $3$ (b) If $G$ is a simple graph with $6$ vertices and the degree of each vertex is at least $3$, then the Hamiltonian cycle exists in $G$ (c) Number of ... $5$ vertices and $7$ edges, then the Hamiltonian cycle exists in $G$ Please help me understand all the options.

asked May 26, 2019 in Graph Theory `JEET 371 views

1 vote

1 answer

15

Made easy Test Series:Graph Theory+Automata
Consider a graph $G$ with $2^{n}$ vertices where the level of each vertex is a $n$ bit binary string represented as $a_{0},a_{1},a_{2},.............,a_{n-1}$, where each $a_{i}$ is $0$ or $1$ ... and $y$ denote the degree of a vertex $G$ and number of connected component of $G$ for $n=8.$ The value of $x+10y$ is_____________

Consider a graph $G$ with $2^{n}$ vertices where the level of each vertex is a $n$ bit binary string represented as $a_{0},a_{1},a_{2},.............,a_{n-1}$, where each $a_{i}$ is $0$ or $1$ ... $x$ and $y$ denote the degree of a vertex $G$ and number of connected component of $G$ for $n=8.$ The value of $x+10y$ is_____________

asked May 23, 2019 in Graph Theory srestha 240 views

5 votes

0 answers

16

IISc CSA - Research Interview Question
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$

Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$

asked May 22, 2019 in Graph Theory ankitgupta.1729 180 views

1 vote

2 answers

17

GateForum Question Bank :Graph Theory
What is the probability that there is an edge in an undirected random graph having 8 vertices? 1 1/8

What is the probability that there is an edge in an undirected random graph having 8 vertices? 1 1/8

asked May 19, 2019 in Graph Theory Hirak 287 views

0 votes

2 answers

18

ACE Workbook:
ACE Workbook: Q) Let G be a simple graph(connected) with minimum number of edges. If G has n vertices with degree-1,2 vertices of degree 2, 4 vertices of degree 3 and 3 vertices of degree-4, then value of n is ? Can anyone give the answer and how to approach these problems. Thanks in advance.

ACE Workbook: Q) Let G be a simple graph(connected) with minimum number of edges. If G has n vertices with degree-1,2 vertices of degree 2, 4 vertices of degree 3 and 3 vertices of degree-4, then value of n is ? Can anyone give the answer and how to approach these problems. Thanks in advance.

asked May 12, 2019 in Graph Theory chandan2teja 164 views

0 votes

3 answers

19

IIIT PGEE 2019
Which of the following gives O(1) complexity if we want to check whether an edge exists between two given nodes in a graph? Adjacency List Adjacency Matrix Incidence Matrix None of these

Which of the following gives O(1) complexity if we want to check whether an edge exists between two given nodes in a graph? Adjacency List Adjacency Matrix Incidence Matrix None of these

asked Apr 29, 2019 in DS manikgupta123 394 views

1 vote

1 answer

20

Difference between DAG and Multi-stage graph
I have trouble understanding the difference between DAG and Multi-stage graph. I know what each of them is But I think that a multi-stage graph is also a DAG. Are multi-stage graphs a special kind of DAG?

I have trouble understanding the difference between DAG and Multi-stage graph. I know what each of them is But I think that a multi-stage graph is also a DAG. Are multi-stage graphs a special kind of DAG?

asked Apr 28, 2019 in Graph Theory gmrishikumar 159 views

0 votes

0 answers

21

ISI2017-PCB-CS-1(b)
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.

Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.

asked Apr 8, 2019 in Graph Theory akash.dinkar12 121 views

0 votes

0 answers

22

Graph Decomposition
What is Graph Decomposition & is it in the syllabus? If it is then please can anyone share some online resources for it. Thank you.

What is Graph Decomposition & is it in the syllabus? If it is then please can anyone share some online resources for it. Thank you.

asked Mar 17, 2019 in Graph Theory noxevolution 71 views

0 votes

0 answers

23

Narsingh deo
What is meant by edge disjoint hamiltonian circuits in a graph

What is meant by edge disjoint hamiltonian circuits in a graph

asked Mar 5, 2019 in Graph Theory Winner 133 views

2 votes

0 answers

24

JEST 2019
A directed graph with n vertices, in which each vertex has exactly 3 outgoing edges. Which one is true? A) All the vertices have indegree = 3 . B) Some vertices will have indegree exactly 3. C)Some vertices have indegree atleast 3. D) Some of the vertices have indegree atmost 3

A directed graph with n vertices, in which each vertex has exactly 3 outgoing edges. Which one is true? A) All the vertices have indegree = 3 . B) Some vertices will have indegree exactly 3. C)Some vertices have indegree atleast 3. D) Some of the vertices have indegree atmost 3

asked Feb 18, 2019 in Graph Theory Sayan Bose 149 views

13 votes

9 answers

25

GATE2019-12
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 $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$

asked Feb 7, 2019 in Graph Theory Arjun 6.1k views

14 votes

6 answers

26

GATE2019-38
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 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

asked Feb 7, 2019 in Graph Theory Arjun 5.9k views

1 vote

0 answers

27

GeeksforGeeks
Let G be a graph with no isolated vertices, and let M be a maximum matching of G. For each vertex v not saturated by M, choose an edge incident to v. Let T be the set of all the chosen edges, and let L = M ∪ T. Which of the following option is TRUE? A L is always ... G. B L is always a minimum edge cover of G. C Both (A) and (B) D Neither (A) nor (B) Can anyone pls help solving this?

Let G be a graph with no isolated vertices, and let M be a maximum matching of G. For each vertex v not saturated by M, choose an edge incident to v. Let T be the set of all the chosen edges, and let L = M ∪ T. Which of the following option is TRUE? A L is always an edge cover of G. B L is always a minimum edge cover of G. C Both (A) and (B) D Neither (A) nor (B) Can anyone pls help solving this?

asked Jan 30, 2019 in Graph Theory Ashish Goyal 207 views

0 votes

2 answers

28

#GRAPH THEORY
A simple regular graph n vertices and 24 edges, find all possible values of n.

A simple regular graph n vertices and 24 edges, find all possible values of n.

asked Jan 29, 2019 in Graph Theory amit166 171 views

0 votes

0 answers

29

Counting

asked Jan 25, 2019 in Graph Theory screddy1313 73 views

0 votes

0 answers

30

Number of sub graphs possible
Number of labelled subgraphs possible for the graph given below______________

Number of labelled subgraphs possible for the graph given below______________

asked Jan 25, 2019 in DS Nandkishor3939 151 views

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

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