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Recent questions tagged degree-of-graph
0
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Degree sequence of graph
Someone please solve it.
GateOverflow04
asked
in
Graph Theory
Jun 30
by
GateOverflow04
142
views
ace-test-series
degree-of-graph
1
vote
1
answer
2
NIELIT Scientific Assistant A 2020 November: 96
In an undirected graph, if we add the degrees of all vertices, it is: odd even cannot be determined always $n+1,$ where $n$ is number of nodes
gatecse
asked
in
Graph Theory
Dec 9, 2020
by
gatecse
173
views
nielit-sta-2020
graph-theory
easy
degree-of-graph
0
votes
1
answer
3
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 $n,d$ $n+d$ $nd$ $nd/2$
Lakshman Patel RJIT
asked
in
Graph Theory
Apr 1, 2020
by
Lakshman Patel RJIT
372
views
nielit2017oct-assistanta-cs
discrete-mathematics
graph-theory
degree-of-graph
0
votes
1
answer
4
NIELIT 2016 MAR Scientist B - Section B: 3
Maximum degree of any node in a simple graph with $n$ vertices is $n-1$ $n$ $n/2$ $n-2$
Lakshman Patel RJIT
asked
in
Graph Theory
Mar 31, 2020
by
Lakshman Patel RJIT
460
views
nielit2016mar-scientistb
discrete-mathematics
graph-theory
degree-of-graph
0
votes
1
answer
5
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 $E$ $2E$ $V$ $2V$
Lakshman Patel RJIT
asked
in
Graph Theory
Mar 30, 2020
by
Lakshman Patel RJIT
8.9k
views
nielit2017july-scientistb-it
discrete-mathematics
graph-theory
degree-of-graph
0
votes
0
answers
6
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
Lakshman Patel RJIT
asked
in
Graph Theory
Mar 30, 2020
by
Lakshman Patel RJIT
899
views
nielit2017july-scientistb-cs
discrete-mathematics
graph-theory
degree-of-graph
0
votes
0
answers
7
Zeal Test Series 2019: Graph Theory - Degree Of Graph
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 ... a vertex of degree 6 and a vertex of degree 7. Which of the following can be the degree of the last vertex ____ ?
Prince Sindhiya
asked
in
Graph Theory
Jan 2, 2019
by
Prince Sindhiya
400
views
zeal
discrete-mathematics
graph-theory
degree-of-graph
zeal19
3
votes
1
answer
8
TIFR CSE 2019 | Part B | Question: 3
A graph is $d$ – regular if every vertex has degree $d$. For a $d$ – regular graph on $n$ vertices, which of the following must be TRUE? $d$ divides $n$ Both $d$ and $n$ are even Both $d$ and $n$ are odd At least one of $d$ and $n$ is odd At least one of $d$ and $n$ is even
Arjun
asked
in
Graph Theory
Dec 18, 2018
by
Arjun
1.2k
views
tifr2019
graph-theory
degree-of-graph
0
votes
0
answers
9
madeesay test series
eyeamgj
asked
in
Graph Theory
Nov 21, 2018
by
eyeamgj
129
views
graph-algorithms
degree-of-graph
30
votes
3
answers
10
TIFR CSE 2018 | Part B | Question: 8
In an undirected graph $G$ with $n$ vertices, vertex $1$ has degree $1$, while each vertex $2,\ldots,n-1$ has degree $10$ and the degree of vertex $n$ is unknown, Which of the following statement must be TRUE on the graph $G$? There is a path ... Vertex $n$ has degree $1$. The diameter of the graph is at most $\frac{n}{10}$ All of the above choices must be TRUE
Arjun
asked
in
Graph Theory
Dec 10, 2017
by
Arjun
4.1k
views
tifr2018
graph-theory
degree-of-graph
2
votes
0
answers
11
Graph Degree sequence : Bondy and Murty : $1.1.16$
Let $d = (d_1,d_2,\dots, d_n)$ be a nonincreasing sequence of nonnegative integers, that is, $d_1 \geq d_2 \geq · · · \geq d_n \geq 0$. Show that: there is a loopless graph with degree sequence d if and only if $\sum_{i=1}^{n}d_i$ is even and $d_1 \leq \sum_{i=2}^{n}d_i$
dd
asked
in
Graph Theory
Jul 5, 2017
by
dd
265
views
graph-theory
non-gate
proof
degree-of-graph
41
votes
9
answers
12
GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
Madhav
asked
in
Graph Theory
Feb 14, 2017
by
Madhav
13.4k
views
gatecse-2017-set2
graph-theory
numerical-answers
degree-of-graph
13
votes
3
answers
13
GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
makhdoom ghaya
asked
in
Graph Theory
Nov 15, 2016
by
makhdoom ghaya
1.2k
views
gate1987
graph-theory
degree-of-graph
descriptive
proof
16
votes
2
answers
14
CMI2015-A-05
An undirected graph has $10$ vertices labelled $1, 2,\dots , 10$ and $37$ edges. Vertices $1, 3, 5, 7, 9$ have degree $8$ and vertices $2, 4, 6, 8$ have degree $7.$ What is the degree of vertex $10$ ? $5$ $6$ $7$ $8$
go_editor
asked
in
Graph Theory
May 27, 2016
by
go_editor
1.5k
views
cmi2015
graph-theory
degree-of-graph
easy
19
votes
6
answers
15
CMI2013-A-06
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 ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$
go_editor
asked
in
Graph Theory
May 23, 2016
by
go_editor
4.6k
views
cmi2013
graph-theory
normal
degree-of-graph
74
votes
5
answers
16
GATE CSE 2006 | Question: 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: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$
go_editor
asked
in
Graph Theory
Apr 24, 2016
by
go_editor
14.2k
views
gatecse-2006
graph-theory
normal
degree-of-graph
3
votes
3
answers
17
Ace Test Series: Graph Theory - Degree Of Graph
How to PROVE S2 is correct?? Consider the statements $S_1$ ) In any simple graph with more than one vertex, there must exist at-least $2$ vetices of the same degree $S_2$ ) A graph with $13$ vertices, $31$ edges, $3$ vertices of degree $5$ and $7$ ... $S_2$ is false C). $S_1$ is false and $S_2$ is true D). Both $S_1$ and $S_2$ are true
Tushar Shinde
asked
in
Graph Theory
Jan 13, 2016
by
Tushar Shinde
817
views
ace-test-series
engineering-mathematics
discrete-mathematics
graph-theory
degree-of-graph
43
votes
3
answers
18
GATE CSE 1991 | Question: 16-b
Show that all vertices in an undirected finite graph cannot have distinct degrees, if the graph has at least two vertices.
Arjun
asked
in
Graph Theory
Nov 15, 2015
by
Arjun
3.1k
views
gate1991
graph-theory
degree-of-graph
descriptive
proof
17
votes
3
answers
19
TIFR CSE 2012 | Part B | Question: 2
In a graph, the degree of a vertex is the number of edges incident (connected) on it. Which of the following is true for every graph $G$? There are even number of vertices of even degree. There are odd number of vertices of even degree ... even number of vertices of odd degree. There are odd number of vertices of odd degree. All the vertices are of even degree.
makhdoom ghaya
asked
in
Graph Theory
Oct 30, 2015
by
makhdoom ghaya
2.2k
views
tifr2012
graph-theory
degree-of-graph
35
votes
6
answers
20
TIFR CSE 2010 | Part B | Question: 36
In a directed graph, every vertex has exactly seven edges coming in. What can one always say about the number of edges going out of its vertices? Exactly seven edges leave every vertex. Exactly seven edges leave some vertex. Some vertex has at least seven edges leaving it. The number of edges coming out of vertex is odd. None of the above.
makhdoom ghaya
asked
in
Graph Theory
Oct 10, 2015
by
makhdoom ghaya
4.3k
views
tifr2010
graph-theory
degree-of-graph
18
votes
3
answers
21
GATE CSE 1995 | Question: 24
Prove that in finite graph, the number of vertices of odd degree is always even.
Kathleen
asked
in
Graph Theory
Oct 8, 2014
by
Kathleen
4.6k
views
gate1995
graph-theory
degree-of-graph
proof
descriptive
35
votes
3
answers
22
GATE CSE 2014 Set 1 | Question: 52
An ordered $n-$tuple $(d_1, d_2,\ldots,d_n)$ with $d_1 \geq d_2 \geq \ldots \geq d_n$ is called graphic if there exists a simple undirected graph with $n$ vertices having degrees $d_1,d_2,\ldots,d_n$ respectively. Which one of the following $6$-tuples is NOT graphic? $(1,1,1,1,1,1)$ $(2,2,2,2,2,2)$ $(3,3,3,1,0,0)$ $(3,2,1,1,1,0)$
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
5.3k
views
gatecse-2014-set1
graph-theory
normal
degree-of-graph
55
votes
4
answers
23
GATE CSE 2006 | Question: 71
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 vertices of degree zero in $G$ is: $1$ $n$ $n + 1$ $2^n$
Rucha Shelke
asked
in
Graph Theory
Sep 26, 2014
by
Rucha Shelke
13.4k
views
gatecse-2006
graph-theory
normal
degree-of-graph
24
votes
2
answers
24
GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q
Arjun
asked
in
Graph Theory
Sep 24, 2014
by
Arjun
14.0k
views
gatecse-2013
graph-theory
easy
degree-of-graph
37
votes
7
answers
25
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
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
15.2k
views
gatecse-2010
graph-theory
degree-of-graph
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