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Recent questions and answers in Graph Theory

37 votes
5 answers
1
GATE2001-2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
answered 15 hours ago in Graph Theory varunrajarathnam 6.2k views
1 vote
4 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 $n(n-1)/2$ $n^{n-2}$ $nx$ $n$
answered 1 day ago in Graph Theory debasish paramanik 467 views
4 votes
2 answers
3
Graph Theory conceptual
A simple graph is one in which there are no self loops and each pair of distinct vertices is connected by at most one edge. Let G be a simple 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 ... a vertex of degree 7. Which of the following can be the degree of the last vertex? (A) 3 (B) 0 (C) 5 (D) 4
A simple graph is one in which there are no self loops and each pair of distinct vertices is connected by at most one edge. Let G be a simple 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 ... 6 and a vertex of degree 7. Which of the following can be the degree of the last vertex? (A) 3 (B) 0 (C) 5 (D) 4
answered Oct 14 in Graph Theory ayush.5 201 views
1 vote
2 answers
7
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_____________
answered Oct 13 in Graph Theory arun yadav 287 views
21 votes
3 answers
8
GATE1990-3-vi
Which of the following graphs is/are planner?
Which of the following graphs is/are planner?
answered Oct 2 in Graph Theory codeitram 2k views
6 votes
3 answers
9
GATE1988-2xvi
Write the adjacency matrix representation of the graph given in below figure.
Write the adjacency matrix representation of the graph given in below figure.
answered Oct 2 in Graph Theory codeitram 1.2k views
23 votes
6 answers
11
TIFR2018-A-9
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
answered Sep 26 in Graph Theory manish_pal_sunny 1.8k views
25 votes
4 answers
12
GATE2008-IT-3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
answered Sep 26 in Graph Theory manish_pal_sunny 3.1k views
7 votes
5 answers
14
ISRO2011-35
How many edges are there in a forest with $v$ vertices and $k$ components? $(v+1) - k$ $(v+1)/2 - k$ $v - k$ $v + k$
How many edges are there in a forest with $v$ vertices and $k$ components? $(v+1) - k$ $(v+1)/2 - k$ $v - k$ $v + k$
answered Sep 18 in Graph Theory Dhruvil 2.7k views
0 votes
2 answers
15
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.
answered Sep 18 in Graph Theory Dhruvil 163 views
8 votes
3 answers
16
GATE1987-9c
Show that the number of odd-degree vertices in a finite graph is even.
Show that the number of odd-degree vertices in a finite graph is even.
answered Sep 15 in Graph Theory KUSHAGRA गुप्ता 575 views
29 votes
4 answers
17
GATE2002-1.4
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 $2$ $3$ $4$ $n-2 \left \lfloor \frac{n}{2} \right \rfloor+2$
answered Sep 14 in Graph Theory Nishisahu 4.9k views
1 vote
1 answer
20
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 89 views
0 votes
2 answers
21
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 140 views
1 vote
1 answer
23
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 106 views
0 votes
1 answer
25
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 127 views
0 votes
1 answer
26
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 114 views
0 votes
1 answer
27
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 82 views
0 votes
1 answer
28
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 103 views
0 votes
1 answer
29
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 75 views
0 votes
1 answer
30
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 62 views
0 votes
1 answer
32
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 131 views
0 votes
3 answers
34
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 315 views
0 votes
7 answers
35
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 304 views
0 votes
2 answers
37
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 238 views
0 votes
1 answer
38
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 247 views
0 votes
1 answer
39
UGCNET-Dec2007-II: 2
The number of edges in a complete graph with $‘n’$ vertices is equal to : $n(n-1)$ $\large\frac{n(n-1)}{2}$ $n^2$ $2n-1$
The number of edges in a complete graph with $‘n’$ vertices is equal to : $n(n-1)$ $\large\frac{n(n-1)}{2}$ $n^2$ $2n-1$
asked Mar 28 in Graph Theory jothee 81 views
0 votes
2 answers
40
UGCNET-Dec2006-II: 3
The number of edges in a complete graph with $N$ vertices is equal to : $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
The number of edges in a complete graph with $N$ vertices is equal to : $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
asked Mar 27 in Graph Theory jothee 151 views
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