Recent questions tagged graph-theory

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1 answer

1

NIELIT 2016 MAR Scientist C - Section B: 20
Degree of each vertex in $K_n$ is $n$ $n-1$ $n-2$ $2n-1$

Degree of each vertex in $K_n$ is $n$ $n-1$ $n-2$ $2n-1$

asked Apr 2 in Graph Theory Lakshman Patel RJIT 54 views

0 votes

1 answer

2

NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 7
The number of the edges in a regular graph of degree $’d’$ and $’n’$ vertices is Maximum of $n,d$ $n+d$ $nd$ $nd/2$

The number of the edges in a regular graph of degree $’d’$ and $’n’$ vertices is Maximum of $n,d$ $n+d$ $nd$ $nd/2$

asked Apr 1 in Graph Theory Lakshman Patel RJIT 96 views

3 votes

3 answers

3

NIELIT 2017 DEC Scientific Assistant A - Section B: 20
Total number of simple graphs that can be drawn using six vertices are: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$

Total number of simple graphs that can be drawn using six vertices are: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$

asked Mar 31 in Graph Theory Lakshman Patel RJIT 192 views

1 vote

1 answer

4

NIELIT 2017 DEC Scientific Assistant A - Section B: 38
If a planner graph, having $25$ vertices divides the plane into $17$ different regions. Then how many edges are used to connect the vertices in this graph. $20$ $30$ $40$ $50$

If a planner graph, having $25$ vertices divides the plane into $17$ different regions. Then how many edges are used to connect the vertices in this graph. $20$ $30$ $40$ $50$

asked Mar 31 in Graph Theory Lakshman Patel RJIT 97 views

0 votes

2 answers

5

NIELIT 2016 MAR Scientist B - Section B: 1
The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is $13$ $14$ $12$ $11$

The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is $13$ $14$ $12$ $11$

asked Mar 31 in Graph Theory Lakshman Patel RJIT 157 views

0 votes

1 answer

6

NIELIT 2016 MAR Scientist B - Section B: 3
Maximum degree of any node in a simple graph with $n$ vertices is $n-1$ $n$ $n/2$ $n-2$

Maximum degree of any node in a simple graph with $n$ vertices is $n-1$ $n$ $n/2$ $n-2$

asked Mar 31 in Graph Theory Lakshman Patel RJIT 105 views

1 vote

1 answer

7

NIELIT 2016 DEC Scientist B (CS) - Section B: 5
Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to: $3$ $4$ $5$ $6$

Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to: $3$ $4$ $5$ $6$

asked Mar 31 in Graph Theory Lakshman Patel RJIT 111 views

0 votes

1 answer

8

NIELIT 2017 July Scientist B (IT) - Section B: 1
Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is $E$ $2E$ $V$ $2V$

Given an undirected graph $G$ with $V$ vertices and $E$ edges, the sum of the degrees of all vertices is $E$ $2E$ $V$ $2V$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 793 views

0 votes

2 answers

9

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 for sparse graphs. Deleting a vertex in adjacency list representation is easier than ... matrix representation. Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.

asked Mar 30 in Graph Theory Lakshman Patel RJIT 193 views

0 votes

1 answer

10

NIELIT 2017 July Scientist B (IT) - Section B: 3
A path in graph $G$, which contains every vertex of $G$ and only once? Euler circuit Hamiltonian path Euler Path Hamiltonian Circuit

A path in graph $G$, which contains every vertex of $G$ and only once? Euler circuit Hamiltonian path Euler Path Hamiltonian Circuit

asked Mar 30 in Graph Theory Lakshman Patel RJIT 138 views

0 votes

1 answer

11

NIELIT 2017 July Scientist B (IT) - Section B: 5
In a given following graph among the following sequences: abeghf abfehg abfhge afghbe Which are depth first traversals of the above graph? I,II and IV only I and IV only II,III and IV only I,III and IV only

In a given following graph among the following sequences: abeghf abfehg abfhge afghbe Which are depth first traversals of the above graph? I,II and IV only I and IV only II,III and IV only I,III and IV only

asked Mar 30 in Graph Theory Lakshman Patel RJIT 121 views

0 votes

1 answer

12

NIELIT 2017 July Scientist B (IT) - Section B: 6
Considering the following graph, which one of the following set of edged represents all the bridges of the given graph? $(a,b), (e,f)$ $(a,b), (a,c)$ $(c,d), (d,h)$ $(a,b)$

Considering the following graph, which one of the following set of edged represents all the bridges of the given graph? $(a,b), (e,f)$ $(a,b), (a,c)$ $(c,d), (d,h)$ $(a,b)$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 85 views

0 votes

1 answer

13

NIELIT 2017 July Scientist B (IT) - Section B: 7
Which of the following statements is/are TRUE? $S1$:The existence of an Euler circuit implies that an Euler path exists. $S2$:The existence of an Euler path implies that an Euler circuit exists. $S1$ is true. $S2$ is true. $S1$ and $S2$ both are true. $S1$ and $S2$ both are false.

Which of the following statements is/are TRUE? $S1$:The existence of an Euler circuit implies that an Euler path exists. $S2$:The existence of an Euler path implies that an Euler circuit exists. $S1$ is true. $S2$ is true. $S1$ and $S2$ both are true. $S1$ and $S2$ both are false.

asked Mar 30 in Graph Theory Lakshman Patel RJIT 106 views

0 votes

1 answer

14

NIELIT 2017 July Scientist B (IT) - Section B: 8
A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is: $5$ $6$ $7$ $8$

A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is: $5$ $6$ $7$ $8$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 78 views

0 votes

1 answer

15

NIELIT 2017 July Scientist B (IT) - Section B: 12
Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is $6$ $8$ $9$ $13$

Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is $6$ $8$ $9$ $13$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 65 views

0 votes

1 answer

16

NIELIT 2017 July Scientist B (IT) - Section B: 15
The number of diagonals that can be drawn by joining the vertices of an octagon is $28$ $48$ $20$ None of the option

The number of diagonals that can be drawn by joining the vertices of an octagon is $28$ $48$ $20$ None of the option

asked Mar 30 in Graph Theory Lakshman Patel RJIT 63 views

0 votes

1 answer

17

NIELIT 2017 July Scientist B (CS) - Section B: 2
Which of the following statements is/are TRUE for an undirected graph? Number of odd degree vertices is even Sum of degrees of all vertices is even P only Q only Both P and Q Neither P nor Q

Which of the following statements is/are TRUE for an undirected graph? Number of odd degree vertices is even Sum of degrees of all vertices is even P only Q only Both P and Q Neither P nor Q

asked Mar 30 in Graph Theory Lakshman Patel RJIT 137 views

0 votes

3 answers

18

NIELIT 2017 July Scientist B (CS) - Section B: 11
Consider the following graph $L$ and find the bridges,if any. No bridge $\{d,e\}$ $\{c,d\}$ $\{c,d\}$ and $\{c,f\}$

Consider the following graph $L$ and find the bridges,if any. No bridge $\{d,e\}$ $\{c,d\}$ $\{c,d\}$ and $\{c,f\}$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 156 views

0 votes

3 answers

19

NIELIT 2017 July Scientist B (CS) - Section B: 12
The following graph has no Euler circuit because It has $7$ vertices. It is even-valent (all vertices have even valence). It is not connected. It does not have a Euler circuit.

The following graph has no Euler circuit because It has $7$ vertices. It is even-valent (all vertices have even valence). It is not connected. It does not have a Euler circuit.

asked Mar 30 in Graph Theory Lakshman Patel RJIT 327 views

0 votes

7 answers

20

NIELIT 2017 July Scientist B (CS) - Section B: 13
For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$

For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$

asked Mar 30 in Graph Theory Lakshman Patel RJIT 326 views

0 votes

4 answers

21

NIELIT 2017 July Scientist B (CS) - Section B: 14
If $G$ is an undirected planar graph on $n$ vertices with $e$ edges then $e\leq n$ $e\leq 2n$ $e\leq 3n$ None of the option

If $G$ is an undirected planar graph on $n$ vertices with $e$ edges then $e\leq n$ $e\leq 2n$ $e\leq 3n$ None of the option

asked Mar 30 in Graph Theory Lakshman Patel RJIT 555 views

0 votes

2 answers

22

NIELIT 2017 July Scientist B (CS) - Section B: 15
Choose the most appropriate definition of plane graph. A simple graph which is isomorphic to hamiltonian graph. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non-empty disjoint subset $X$ and ... in a plane in such a way that any pair of edges meet only at their end vertices. None of the option.

Choose the most appropriate definition of plane graph. A simple graph which is isomorphic to hamiltonian graph. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non-empty disjoint subset $X$ and $Y$ in such a way that each edge ... . A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices. None of the option.

asked Mar 30 in Graph Theory Lakshman Patel RJIT 254 views

0 votes

1 answer

23

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 274 views

1 vote

4 answers

24

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 506 views

0 votes

1 answer

25

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 158 views

6 votes

3 answers

26

GATE 2020 CSE | 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 _______

asked Feb 12 in Graph Theory Arjun 2.3k views

0 votes

3 answers

27

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 241 views

2 votes

1 answer

28

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 190 views

5 votes

2 answers

29

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 179 views

1 vote

1 answer

30

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 132 views

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