Discrete math ( graphs, trees and tours)
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Can someone check with me if my answer is right for this question?
I got $n(n+1)/2$ .
The question is posted below.
$newcommand{Barbell}{operatorname{Barbell}}$
For $n$ an integer with $n ≥ 3$, let $Barbell(n)$ be the graph that is made by attaching with a single edge two complete graphs with $n$ vertices each. A complete graph with $n$ vertices is a graph in which every vertex is adjacent to every other vertex besides itself.
The following question is about $Barbell(n)$. For an integer $n ≥ 3$, how many edges are in the graph $Barbell(n)$?
discrete-mathematics
edited Nov 13 at 5:26
C.Ding
1,2311321
asked Nov 13 at 4:49
Embagaliano Asmara
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
Can someone check with me if my answer is right for this question?
I got $n(n+1)/2$ .
The question is posted below.
$newcommand{Barbell}{operatorname{Barbell}}$
For $n$ an integer with $n ≥ 3$, let $Barbell(n)$ be the graph that is made by attaching with a single edge two complete graphs with $n$ vertices each. A complete graph with $n$ vertices is a graph in which every vertex is adjacent to every other vertex besides itself.
The following question is about $Barbell(n)$. For an integer $n ≥ 3$, how many edges are in the graph $Barbell(n)$?
discrete-mathematics
edited Nov 13 at 5:26
C.Ding
1,2311321
asked Nov 13 at 4:49
Embagaliano Asmara
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
This looks like a homework problem. Have you tried anything?
– Robert Thingum
Nov 13 at 4:51
I tried it. I got n(n+1)/2, but I am not sure. By the way it is not a homework problem. It is just practice problems for midterm.
– Embagaliano Asmara
Nov 13 at 4:54
Try drawing Barbell$(3)$. Does the number of edges match up with what your answer says it should be?
– Robert Thingum
Nov 13 at 5:03
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Can someone check with me if my answer is right for this question?
I got $n(n+1)/2$ .
The question is posted below.
$newcommand{Barbell}{operatorname{Barbell}}$
For $n$ an integer with $n ≥ 3$, let $Barbell(n)$ be the graph that is made by attaching with a single edge two complete graphs with $n$ vertices each. A complete graph with $n$ vertices is a graph in which every vertex is adjacent to every other vertex besides itself.
The following question is about $Barbell(n)$. For an integer $n ≥ 3$, how many edges are in the graph $Barbell(n)$?
discrete-mathematics
edited Nov 13 at 5:26
C.Ding
1,2311321
asked Nov 13 at 4:49
Embagaliano Asmara
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Can someone check with me if my answer is right for this question?
I got $n(n+1)/2$ .
The question is posted below.
$newcommand{Barbell}{operatorname{Barbell}}$
For $n$ an integer with $n ≥ 3$, let $Barbell(n)$ be the graph that is made by attaching with a single edge two complete graphs with $n$ vertices each. A complete graph with $n$ vertices is a graph in which every vertex is adjacent to every other vertex besides itself.
The following question is about $Barbell(n)$. For an integer $n ≥ 3$, how many edges are in the graph $Barbell(n)$?
discrete-mathematics
discrete-mathematics
edited Nov 13 at 5:26
C.Ding
1,2311321
asked Nov 13 at 4:49
Embagaliano Asmara
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 13 at 5:26
C.Ding
1,2311321
asked Nov 13 at 4:49
Embagaliano Asmara
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 13 at 5:26
C.Ding
1,2311321
edited Nov 13 at 5:26
C.Ding
1,2311321
edited Nov 13 at 5:26
C.Ding
1,2311321
1,2311321
asked Nov 13 at 4:49
Embagaliano Asmara
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 4:49
Embagaliano Asmara
61
asked Nov 13 at 4:49
Embagaliano Asmara
61
61
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Embagaliano Asmara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
This looks like a homework problem. Have you tried anything?
– Robert Thingum
Nov 13 at 4:51
I tried it. I got n(n+1)/2, but I am not sure. By the way it is not a homework problem. It is just practice problems for midterm.
– Embagaliano Asmara
Nov 13 at 4:54
Try drawing Barbell$(3)$. Does the number of edges match up with what your answer says it should be?
– Robert Thingum
Nov 13 at 5:03
add a comment |
1
This looks like a homework problem. Have you tried anything?
– Robert Thingum
Nov 13 at 4:51
I tried it. I got n(n+1)/2, but I am not sure. By the way it is not a homework problem. It is just practice problems for midterm.
– Embagaliano Asmara
Nov 13 at 4:54
Try drawing Barbell$(3)$. Does the number of edges match up with what your answer says it should be?
– Robert Thingum
Nov 13 at 5:03
1
1
This looks like a homework problem. Have you tried anything?
– Robert Thingum
Nov 13 at 4:51
This looks like a homework problem. Have you tried anything?
– Robert Thingum
Nov 13 at 4:51
I tried it. I got n(n+1)/2, but I am not sure. By the way it is not a homework problem. It is just practice problems for midterm.
– Embagaliano Asmara
Nov 13 at 4:54
I tried it. I got n(n+1)/2, but I am not sure. By the way it is not a homework problem. It is just practice problems for midterm.
– Embagaliano Asmara
Nov 13 at 4:54
Try drawing Barbell$(3)$. Does the number of edges match up with what your answer says it should be?
– Robert Thingum
Nov 13 at 5:03
Try drawing Barbell$(3)$. Does the number of edges match up with what your answer says it should be?
– Robert Thingum
Nov 13 at 5:03
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
To clarify, given $ngeq 3$ you are given two graphs $G_{1}$ and $G_{2}$, each of which is a copy of the complete graph on $n$ vertices, $K_{n}$. The graph Barbell$(n)$ is then formed by choosing a vertex $v_{1}in G_{1}$ and a vertex $v_{2}in G_{2}$ and then adding an edge between $v_{1}$ and $v_{2}$ to connect $G_{1}$ and $G_{2}$ together.
Hint:
How many edges are in $K_{n}$?
$K_{2}$ has $1$ edge.
$K_{3}$ has $3$ edges.
$K_{4}$ has $6$ edges.
In general there are as many edges in $K_{n}$ as there are ways of choosing a subset of size $2$ out of the set ${1,2,ldots,n}$.
If the number of edges in $K_{n}$ is $E(n)$ then the answer to your problem is $2E(n)+1$.
answered Nov 13 at 4:54
Robert Thingum
7141316
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
To clarify, given $ngeq 3$ you are given two graphs $G_{1}$ and $G_{2}$, each of which is a copy of the complete graph on $n$ vertices, $K_{n}$. The graph Barbell$(n)$ is then formed by choosing a vertex $v_{1}in G_{1}$ and a vertex $v_{2}in G_{2}$ and then adding an edge between $v_{1}$ and $v_{2}$ to connect $G_{1}$ and $G_{2}$ together.
Hint:
How many edges are in $K_{n}$?
$K_{2}$ has $1$ edge.
$K_{3}$ has $3$ edges.
$K_{4}$ has $6$ edges.
In general there are as many edges in $K_{n}$ as there are ways of choosing a subset of size $2$ out of the set ${1,2,ldots,n}$.
If the number of edges in $K_{n}$ is $E(n)$ then the answer to your problem is $2E(n)+1$.
answered Nov 13 at 4:54
Robert Thingum
7141316
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
add a comment |
up vote
0
down vote
To clarify, given $ngeq 3$ you are given two graphs $G_{1}$ and $G_{2}$, each of which is a copy of the complete graph on $n$ vertices, $K_{n}$. The graph Barbell$(n)$ is then formed by choosing a vertex $v_{1}in G_{1}$ and a vertex $v_{2}in G_{2}$ and then adding an edge between $v_{1}$ and $v_{2}$ to connect $G_{1}$ and $G_{2}$ together.
Hint:
How many edges are in $K_{n}$?
$K_{2}$ has $1$ edge.
$K_{3}$ has $3$ edges.
$K_{4}$ has $6$ edges.
In general there are as many edges in $K_{n}$ as there are ways of choosing a subset of size $2$ out of the set ${1,2,ldots,n}$.
If the number of edges in $K_{n}$ is $E(n)$ then the answer to your problem is $2E(n)+1$.
answered Nov 13 at 4:54
Robert Thingum
7141316
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
add a comment |
up vote
0
down vote
up vote
0
down vote
To clarify, given $ngeq 3$ you are given two graphs $G_{1}$ and $G_{2}$, each of which is a copy of the complete graph on $n$ vertices, $K_{n}$. The graph Barbell$(n)$ is then formed by choosing a vertex $v_{1}in G_{1}$ and a vertex $v_{2}in G_{2}$ and then adding an edge between $v_{1}$ and $v_{2}$ to connect $G_{1}$ and $G_{2}$ together.
Hint:
How many edges are in $K_{n}$?
$K_{2}$ has $1$ edge.
$K_{3}$ has $3$ edges.
$K_{4}$ has $6$ edges.
In general there are as many edges in $K_{n}$ as there are ways of choosing a subset of size $2$ out of the set ${1,2,ldots,n}$.
If the number of edges in $K_{n}$ is $E(n)$ then the answer to your problem is $2E(n)+1$.
answered Nov 13 at 4:54
Robert Thingum
7141316
To clarify, given $ngeq 3$ you are given two graphs $G_{1}$ and $G_{2}$, each of which is a copy of the complete graph on $n$ vertices, $K_{n}$. The graph Barbell$(n)$ is then formed by choosing a vertex $v_{1}in G_{1}$ and a vertex $v_{2}in G_{2}$ and then adding an edge between $v_{1}$ and $v_{2}$ to connect $G_{1}$ and $G_{2}$ together.
Hint:
How many edges are in $K_{n}$?
$K_{2}$ has $1$ edge.
$K_{3}$ has $3$ edges.
$K_{4}$ has $6$ edges.
In general there are as many edges in $K_{n}$ as there are ways of choosing a subset of size $2$ out of the set ${1,2,ldots,n}$.
If the number of edges in $K_{n}$ is $E(n)$ then the answer to your problem is $2E(n)+1$.
answered Nov 13 at 4:54
Robert Thingum
7141316
answered Nov 13 at 4:54
Robert Thingum
7141316
answered Nov 13 at 4:54
Robert Thingum
7141316
answered Nov 13 at 4:54
Robert Thingum
7141316
7141316
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
add a comment |
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
where is that +1 coming from
– Embagaliano Asmara
Nov 13 at 5:17
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
The $+1$ is coming from the edge you use to connect the two graphs. It is the "bar" of the barbell.
– Robert Thingum
Nov 13 at 5:18
add a comment |
Embagaliano Asmara is a new contributor. Be nice, and check out our Code of Conduct.
Embagaliano Asmara is a new contributor. Be nice, and check out our Code of Conduct.
Embagaliano Asmara is a new contributor. Be nice, and check out our Code of Conduct.
Embagaliano Asmara is a new contributor. Be nice, and check out our Code of Conduct.
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1
This looks like a homework problem. Have you tried anything?
– Robert Thingum
Nov 13 at 4:51
I tried it. I got n(n+1)/2, but I am not sure. By the way it is not a homework problem. It is just practice problems for midterm.
– Embagaliano Asmara
Nov 13 at 4:54
Try drawing Barbell$(3)$. Does the number of edges match up with what your answer says it should be?
– Robert Thingum
Nov 13 at 5:03