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Degree sequence of graph
Someone please solve it.
GateOverflow04
asked
in
Graph Theory
6 days
ago
by
GateOverflow04
30
views
ace-test-series
degree-of-graph
0
votes
1
answer
2
Doubt:
Let “m” be the number of edges, “n” the number of vertices and “k” the number of connected components of a graph G. Prove that: $\left ( n-k \right )\leq m\leq \frac{\left ( n-k \right )\left ( n-k+1 \right )}{2}$ Why least number of edges are $\left ( n-k \right )$ and Why most number of edges are $\frac{\left ( n-k \right )\left ( n-k+1 \right )}{2}$ ? What is the idea behind this prove?
Simmi Kaur
asked
in
Graph Theory
Jun 28
by
Simmi Kaur
●
2
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13
●
15
36
views
graph-connectivity
3
votes
2
answers
3
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 1
How many words can be formed by re-arranging the letters of the word “PROBLEMS” such that $P$ and $S$ occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
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5
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130
●
164
121
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
1-mark
4
votes
1
answer
4
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 2
A set of cards is numbered $1$ through $6.$ Quantity A: The number of ways to pick $3$ of the $6$ cards such that card number $1$ ... Quantity B is greater than Quantity A. The two quantities are equal. The relationship cannot be determined from the information given.
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
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130
●
164
101
views
goclasses_wq13
goclasses
combinatory
counting
1-mark
4
votes
2
answers
5
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 3
Consider the following two combinatorial identities: For all $\mathrm{k}, \mathrm{n} \in \mathrm{N}$ with $\mathrm{k} \leq \mathrm{n}$ ... $1$ Only $2$ Both None
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
82
views
goclasses_wq13
goclasses
combinatory
counting
1-mark
3
votes
1
answer
6
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 4
We go to a pizza party, and there are $5$ types of pizza. We have been starving for days, so we can eat $13$ slices, but we want to sample each type at least once. In how many ways can we do this? Order does not matter.
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
97
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
1-mark
3
votes
1
answer
7
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 5
How many integer solutions does the equation $ x_{1}+x_{2}+x_{3}+x_{4}=15 $ have, if we require that $x_{1} \geq 2, x_{2} \geq 3, x_{3} \geq 10$ and $x_{4} \geq-3 ?$
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
61
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
1-mark
4
votes
1
answer
8
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 6
How many integer solutions are there to the system of inequalities $ x_{1}+x_{2}+x_{3}+x_{4} \leq 15, \quad x_{1}, \ldots, x_{4} \geq 0 ? $
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
73
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
1-mark
5
votes
3
answers
9
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 7
We want those bit strings of length $10$ which Start and end with the symbol $1.$ No two zeroes are consecutive. How many such bit strings are there?
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
195
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
3
votes
1
answer
10
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 8
How many ways are there to split a dozen people into $3$ teams, where one team has $2$ people, and the other two teams have $5$ people each?
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
101
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
6
votes
1
answer
11
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 9
A student is given an exam consisting of $8$ essay questions divided into $4$ groups of $2$ questions each. The student is required to select a set of $6$ questions to answer, including at least $1$ question from each of the $4$ groups. How many sets of questions satisfy this requirement?
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
197
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
5
votes
1
answer
12
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 10
In how many rearrangements of the letters of the word SCINTILLATING will no two 'I's appear together? ${ }^{11} \mathrm{C}_{3} * 13!$ $\frac{10 !}{2 ! * 2 ! * 2 !}$ ${ }^{11} \mathrm{C}_{3} * 3 ! * 10 !$ ${ }^{11} \mathrm{C}_{3} \frac{10 !}{2 ! * 2 ! * 2 !}$
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
93
views
goclasses_wq13
goclasses
combinatory
counting
2-marks
3
votes
2
answers
13
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 11
How many squares are there in a chess board? $64$ $204$ $1296$ $4096$
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
149
views
goclasses_wq13
goclasses
combinatory
counting
2-marks
2
votes
1
answer
14
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 12
How many rectangles are there in a chess board?
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
72
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
2
votes
1
answer
15
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 13
For which of the following events will the number of outcomes exceed $50?$(Indicate all such events.) The number of outcomes in which at least three heads appear in $6$ consecutive tosses of a fair coin. ... number of outcomes in which all the vowels appear together when the letters of the word 'PRIORITY' are reordered.
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
56
views
goclasses_wq13
goclasses
combinatory
counting
multiple-selects
2-marks
2
votes
2
answers
16
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 14
The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
69
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
2
votes
1
answer
17
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 15
In an examination, a question paper consists of $12$ questions divided into two parts i.e, Part I and Part II, containing $5$ and $7$ questions respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
74
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
6
votes
1
answer
18
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 16
Count the number of non-negative integer solutions to $ 3 x_{1}+3 x_{2}+3 x_{3}+7 x_{4}=22 . $
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
●
5
●
130
●
164
132
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
2
votes
1
answer
19
no of solutions to the following inequality 12 <= w + x + y + z <= 14
No. of solutions to the following inequality 12 <= w + x + y + z <= 14 where w,x,y,z>=0
khushitshah
asked
in
Combinatory
Jun 8
by
khushitshah
●
1
72
views
combinatory
discrete-mathematics
counting
0
votes
1
answer
20
Can someone please explain how "I am lying" is a Liars paradox? and how the truth values are toggling here?
Roy12
asked
in
Mathematical Logic
Jun 8
by
Roy12
55
views
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