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Recent questions and answers in Graph Theory
41
votes
7
answers
1
TIFR2017-B-12
An undirected graph is complete if there is an edge between every pair of vertices. Given a complete undirected graph on $n$ vertices, in how many ways can you choose a direction for the edges so that there are no directed cycles? $n$ $\frac{n(n-1)}{2}$ $n!$ $2^n$ $2^m, \: \text{ where } m=\frac{n(n-1)}{2}$
An undirected graph is complete if there is an edge between every pair of vertices. Given a complete undirected graph on $n$ vertices, in how many ways can you choose a direction for the edges so that there are no directed cycles? $n$ $\frac{n(n-1)}{2}$ $n!$ $2^n$ $2^m, \: \text{ where } m=\frac{n(n-1)}{2}$
answered
4 hours
ago
in
Graph Theory
reboot
3.2k
views
tifr2017
graph-theory
counting
0
votes
1
answer
2
Zeal Test Series 2019: Graph theory - Vertex Cover
is there any easy way to do this i did it by making equation,Mn+Ec=Vn, Vc+In=Vn
is there any easy way to do this i did it by making equation,Mn+Ec=Vn, Vc+In=Vn
answered
Jan 20
in
Graph Theory
Jan Bhardwaj
172
views
zeal
graph-theory
vertex-cover
zeal2019
1
vote
1
answer
3
Ace Test Series: Graph Theory - Counting
Number of multi-graphs possible with 4 vertices and at most 2 edges between each pair of vertices is ________________
Number of multi-graphs possible with 4 vertices and at most 2 edges between each pair of vertices is ________________
answered
Dec 29, 2020
in
Graph Theory
Karan Negi
338
views
ace-test-series
graph-theory
counting
78
votes
9
answers
4
GATE2014-1-51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
answered
Dec 17, 2020
in
Graph Theory
ashutoshbsathe
13.2k
views
gate2014-1
graph-theory
numerical-answers
normal
graph-connectivity
0
votes
2
answers
5
GAte zeal mock
I got 41 as answer please verify
I got 41 as answer please verify
answered
Dec 9, 2020
in
Graph Theory
eshita1997
209
views
minimum-spanning-trees
22
votes
5
answers
6
GATE2018-18
The chromatic number of the following graph is _____
The chromatic number of the following graph is _____
answered
Dec 6, 2020
in
Graph Theory
Raj Bopche
5.5k
views
graph-theory
graph-coloring
numerical-answers
gate2018
46
votes
4
answers
7
GATE2003-8, ISRO2009-53
Let $G$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $G$, 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 $G$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $G$, 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 $n-k$
answered
Dec 4, 2020
in
Graph Theory
StoneHeart
7.7k
views
gate2003
graph-theory
graph-connectivity
normal
isro2009
36
votes
4
answers
8
GATE2010-1
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with $\xi(S) = \xi(T)$, then $| S| = 2| T |$ $| S | = | T | - 1$ $| S| = | T | $ $| S | = | T| + 1$
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with $\xi(S) = \xi(T)$, then $| S| = 2| T |$ $| S | = | T | - 1$ $| S| = | T | $ $| S | = | T| + 1$
answered
Nov 28, 2020
in
Graph Theory
StoneHeart
5.8k
views
gate2010
graph-theory
normal
trees
40
votes
4
answers
9
GATE2013-26
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 $e$ and $e'$ ... graph of a 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 $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if $e$ and $e'$ are ... line graph of a 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
answered
Nov 28, 2020
in
Graph Theory
StoneHeart
9.1k
views
gate2013
graph-theory
normal
line-graph
27
votes
4
answers
10
GATE2008-23
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$
answered
Nov 28, 2020
in
Graph Theory
StoneHeart
6k
views
gate2008
graph-theory
normal
graph-planarity
60
votes
5
answers
11
GATE2006-72
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 maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
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 maximum degree of a vertex in $G$ is: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
answered
Nov 27, 2020
in
Graph Theory
StoneHeart
8.6k
views
gate2006
graph-theory
normal
degree-of-graph
56
votes
5
answers
12
GATE2004-79
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 ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k\\$ $^{\left(\frac{n^2-n}{2}\right)}C_n\\$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
answered
Nov 27, 2020
in
Graph Theory
StoneHeart
7.4k
views
gate2004
graph-theory
combinatory
normal
counting
0
votes
4
answers
13
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 $\{c,f\}$
answered
Nov 6, 2020
in
Graph Theory
Ashwani Kumar 2
378
views
nielit2017july-scientistb-cs
discrete-mathematics
graph-theory
bridges
48
votes
10
answers
14
GATE1994-1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
answered
Oct 31, 2020
in
Graph Theory
rupesh17
17.1k
views
gate1994
graph-theory
combinatory
normal
isro2008
counting
22
votes
5
answers
15
GATE2015-1-54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
answered
Oct 27, 2020
in
Graph Theory
prajjwalsingh_11
9.2k
views
gate2015-1
graph-theory
graph-connectivity
normal
graph-planarity
out-of-syllabus-now
numerical-answers
37
votes
5
answers
16
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
Oct 25, 2020
in
Graph Theory
varunrajarathnam
7.4k
views
gate2001
graph-theory
normal
counting
1
vote
4
answers
17
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
Oct 24, 2020
in
Graph Theory
debasish paramanik
947
views
nielit2017dec-scientistb
discrete-mathematics
graph-theory
graph-coloring
4
votes
2
answers
18
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, 2020
in
Graph Theory
ayush.5
285
views
graph-theory
discrete-mathematics
0
votes
2
answers
19
Gateforum Test Series: Graph Theory - Graph Matching
answered
Oct 14, 2020
in
Graph Theory
wander
248
views
gateforum-test-series
discrete-mathematics
graph-theory
graph-matching
0
votes
2
answers
20
ME test series question on graph theory
answered
Oct 13, 2020
in
Graph Theory
arun yadav
173
views
graph-theory
0
votes
2
answers
21
Zeal Test Series 2019: Graph Theory - Graph Connectivity
answered
Oct 13, 2020
in
Graph Theory
arun yadav
301
views
zeal
graph-theory
graph-connectivity
zeal2019
2
votes
2
answers
22
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, 2020
in
Graph Theory
arun yadav
364
views
made-easy-test-series
graph-theory
theory-of-computation
24
votes
3
answers
23
GATE1990-3-vi
Which of the following graphs is/are planner?
Which of the following graphs is/are planner?
answered
Oct 2, 2020
in
Graph Theory
codeitram
3.1k
views
gate1989
normal
graph-theory
graph-planarity
descriptive
6
votes
3
answers
24
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, 2020
in
Graph Theory
codeitram
1.6k
views
gate1988
descriptive
graph-theory
graph-connectivity
0
votes
1
answer
25
Gateforum Test Series: Graph Theory - Graph connectivity
answered
Sep 28, 2020
in
Graph Theory
Vineet Pandey
217
views
discrete-mathematics
graph-theory
gateforum-test-series
graph-connectivity
25
votes
6
answers
26
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, 2020
in
Graph Theory
manish_pal_sunny
2.3k
views
tifr2018
graph-theory
graph-coloring
26
votes
4
answers
27
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, 2020
in
Graph Theory
manish_pal_sunny
3.9k
views
gate2008-it
graph-theory
graph-coloring
normal
3
votes
3
answers
28
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: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$
answered
Sep 20, 2020
in
Graph Theory
Himanshu Kumar Gupta
571
views
nielit2017dec-assistanta
discrete-mathematics
graph-theory
7
votes
5
answers
29
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, 2020
in
Graph Theory
Dhruvil
2.9k
views
isro2011
graph-theory
0
votes
2
answers
30
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, 2020
in
Graph Theory
Dhruvil
1.6k
views
nielit2017july-scientistb-it
discrete-mathematics
graph-theory
9
votes
3
answers
31
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, 2020
in
Graph Theory
KUSHAGRA गुप्ता
738
views
gate1987
graph-theory
degree-of-graph
descriptive
30
votes
4
answers
32
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, 2020
in
Graph Theory
Nishisahu
5.8k
views
gate2002
graph-theory
graph-coloring
normal
0
votes
1
answer
33
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, 2020
in
Graph Theory
Lakshman Patel RJIT
116
views
nielit2016mar-scientistc
discrete-mathematics
graph-theory
0
votes
1
answer
34
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, 2020
in
Graph Theory
Lakshman Patel RJIT
154
views
nielit2017oct-assistanta-cs
discrete-mathematics
graph-theory
degree-of-graph
1
vote
1
answer
35
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, 2020
in
Graph Theory
Lakshman Patel RJIT
228
views
nielit2017dec-assistanta
discrete-mathematics
graph-theory
graph-planarity
0
votes
2
answers
36
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, 2020
in
Graph Theory
Lakshman Patel RJIT
412
views
nielit2016mar-scientistb
discrete-mathematics
graph-theory
0
votes
1
answer
37
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, 2020
in
Graph Theory
Lakshman Patel RJIT
178
views
nielit2016mar-scientistb
discrete-mathematics
graph-theory
degree-of-graph
1
vote
1
answer
38
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, 2020
in
Graph Theory
Lakshman Patel RJIT
207
views
nielit2016dec-scientistb-cs
discrete-mathematics
graph-theory
graph-planarity
0
votes
1
answer
39
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, 2020
in
Graph Theory
Lakshman Patel RJIT
1.9k
views
nielit2017july-scientistb-it
discrete-mathematics
graph-theory
degree-of-graph
0
votes
1
answer
40
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
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Mar 30, 2020
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Graph Theory
Lakshman Patel RJIT
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nielit2017july-scientistb-it
discrete-mathematics
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