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Recent questions tagged degreeofgraph
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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 ____ ?
asked
Jan 2
in
Graph Theory
by
Prince Sindhiya
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5.6k
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zeal
discretemathematics
graphtheory
degreeofgraph
zeal19
+14
votes
2
answers
2
TIFR2018B8
In an undirected graph $G$ with $n$ vertices, vertex $1$ has degree $1$, while each vertex $2,\ldots,n1$ 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 from vertex $1$ to ... $n$ has degree $1$. The diameter of the graph is at most $\frac{n}{10}$ All of the above choices must be TRUE
asked
Dec 10, 2017
in
Graph Theory
by
Arjun
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423k
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836
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tifr2018
graphtheory
degreeofgraph
+1
vote
1
answer
3
virtualgate
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, ... 6 and a vertex of degree 7. Which of the following can be the degree of the last vertex? A) 4 B) 0 C) 3 D) 5
asked
Nov 19, 2017
in
Graph Theory
by
Manoja Rajalakshmi A
Boss
(
11.4k
points)

68
views
degreeofgraph
+24
votes
8
answers
4
GATE2017223
$G$ 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 _________ .
asked
Feb 14, 2017
in
Graph Theory
by
Madhav
Active
(
1.6k
points)

4.6k
views
gate20172
graphtheory
numericalanswers
degreeofgraph
+6
votes
2
answers
5
GATE19879c
Show that the number of odddegree vertices in a finite graph is even.
asked
Nov 15, 2016
in
Graph Theory
by
makhdoom ghaya
Boss
(
29.9k
points)

325
views
gate1987
graphtheory
degreeofgraph
descriptive
+14
votes
1
answer
6
CMI2015A05
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 $10$ ? $5$ $6$ $7$ $8$
asked
May 27, 2016
in
Graph Theory
by
jothee
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(
104k
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376
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cmi2015
graphtheory
degreeofgraph
easy
+13
votes
3
answers
7
CMI2013A06
A simple graph is one in which there are no selfloops 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? $3$ $0$ $5$ $4$
asked
May 23, 2016
in
Graph Theory
by
jothee
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(
104k
points)

727
views
cmi2013
graphtheory
normal
degreeofgraph
+45
votes
4
answers
8
GATE200672
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: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n2}$ $2^{n3}\times 3$ $2^{n1}$
asked
Apr 24, 2016
in
Graph Theory
by
jothee
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(
104k
points)

4.4k
views
gate2006
graphtheory
normal
degreeofgraph
+3
votes
3
answers
9
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 atleast $2$ 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
asked
Jan 13, 2016
in
Graph Theory
by
Tushar Shinde
Active
(
2.2k
points)

465
views
acetestseries
engineeringmathematics
discretemathematics
graphtheory
degreeofgraph
+29
votes
3
answers
10
GATE199116b
Show that all vertices in an undirected finite graph cannot have distinct degrees, if the graph has at least two vertices.
asked
Nov 15, 2015
in
Graph Theory
by
Arjun
Veteran
(
423k
points)

1.1k
views
gate1991
graphtheory
degreeofgraph
descriptive
+11
votes
2
answers
11
TIFR2012B2
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. There are even number of vertices of odd degree. There are odd number of vertices of odd degree. All the vertices are of even degree.
asked
Oct 30, 2015
in
Graph Theory
by
makhdoom ghaya
Boss
(
29.9k
points)

499
views
tifr2012
graphtheory
degreeofgraph
+23
votes
5
answers
12
TIFR2010B36
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.
asked
Oct 10, 2015
in
Graph Theory
by
makhdoom ghaya
Boss
(
29.9k
points)

1.2k
views
tifr2010
graphtheory
degreeofgraph
+15
votes
2
answers
13
GATE199524
Prove that in finite graph, the number of vertices of odd degree is always even.
asked
Oct 8, 2014
in
Graph Theory
by
Kathleen
Veteran
(
52.1k
points)

1.3k
views
gate1995
graphtheory
degreeofgraph
descriptive
+24
votes
3
answers
14
GATE2014152
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? $(1,1,1,1,1,1)$ $(2,2,2,2,2,2)$ $(3,3,3,1,0,0)$ $(3,2,1,1,1,0)$
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
104k
points)

2.1k
views
gate20141
graphtheory
normal
degreeofgraph
+35
votes
4
answers
15
GATE200671
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: $1$ $n$ $n + 1$ $2^n$
asked
Sep 26, 2014
in
Graph Theory
by
Rucha Shelke
Active
(
3.3k
points)

4.9k
views
gate2006
graphtheory
normal
degreeofgraph
+17
votes
2
answers
16
GATE201325
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
asked
Sep 24, 2014
in
Graph Theory
by
Arjun
Veteran
(
423k
points)

2.7k
views
gate2013
graphtheory
easy
degreeofgraph
+25
votes
6
answers
17
GATE201028
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
asked
Sep 21, 2014
in
Graph Theory
by
gatecse
Boss
(
16.7k
points)

4.8k
views
gate2010
graphtheory
degreeofgraph
+37
votes
7
answers
18
GATE200340
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid  6$. The mindegree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, mindegree of $G$ cannot be $3$ $4$ $5$ $6$
asked
Sep 17, 2014
in
Graph Theory
by
Kathleen
Veteran
(
52.1k
points)

3.8k
views
gate2003
graphtheory
normal
degreeofgraph
+31
votes
3
answers
19
GATE20093
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
asked
Sep 15, 2014
in
Graph Theory
by
gatecse
Boss
(
16.7k
points)

2.2k
views
gate2009
graphtheory
normal
degreeofgraph
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