Is there a math term for a modificated minimum spanning tree?
$begingroup$
I have found a minimum spanning tree (left figure).
Then I have applied some modification:
- The edge
A-B(red) was added, - The edge
C-D(green) was rewritten toC'-D.
Edit. I don't delete the vertices.
- Steps 1-2 can be repeated more that one time for different edges.
Question. Is there a math term for an obtained graph (right figure)?
graph-theory notation terminology
asked Dec 4 '18 at 2:47
NickNick
301112
$endgroup$
add a comment |
$begingroup$
I have found a minimum spanning tree (left figure).
Then I have applied some modification:
- The edge
A-B(red) was added, - The edge
C-D(green) was rewritten toC'-D.
Edit. I don't delete the vertices.
- Steps 1-2 can be repeated more that one time for different edges.
Question. Is there a math term for an obtained graph (right figure)?
graph-theory notation terminology
asked Dec 4 '18 at 2:47
NickNick
301112
$endgroup$
add a comment |
$begingroup$
I have found a minimum spanning tree (left figure).
Then I have applied some modification:
- The edge
A-B(red) was added, - The edge
C-D(green) was rewritten toC'-D.
Edit. I don't delete the vertices.
- Steps 1-2 can be repeated more that one time for different edges.
Question. Is there a math term for an obtained graph (right figure)?
graph-theory notation terminology
asked Dec 4 '18 at 2:47
NickNick
301112
$endgroup$
I have found a minimum spanning tree (left figure).
Then I have applied some modification:
- The edge
A-B(red) was added, - The edge
C-D(green) was rewritten toC'-D.
Edit. I don't delete the vertices.
- Steps 1-2 can be repeated more that one time for different edges.
Question. Is there a math term for an obtained graph (right figure)?
graph-theory notation terminology
graph-theory notation terminology
asked Dec 4 '18 at 2:47
NickNick
301112
asked Dec 4 '18 at 2:47
NickNick
301112
edited Dec 4 '18 at 15:35
Nick
asked Dec 4 '18 at 2:47
NickNick
301112
asked Dec 4 '18 at 2:47
NickNick
301112
asked Dec 4 '18 at 2:47
NickNick
301112
301112
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Well...it's no longer a tree, so I guess the best I can say is that it's a spanning subgraph. I'm not sure whether your "modifications" always preserve the property that the new graph contains all the vertices. If not, then you can just say "it's a subgraph."
$endgroup$
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
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It is more than a subgraph : it is a $1$-tree.
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– Kuifje
Dec 4 '18 at 8:48
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In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
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– John Hughes
Dec 4 '18 at 12:22
add a comment |
$begingroup$
There is a term for this subgraph with a unique cycle: it is a $1$-tree.
Some authors also call it a pseudotree.
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
$endgroup$
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Well...it's no longer a tree, so I guess the best I can say is that it's a spanning subgraph. I'm not sure whether your "modifications" always preserve the property that the new graph contains all the vertices. If not, then you can just say "it's a subgraph."
$endgroup$
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
$begingroup$
It is more than a subgraph : it is a $1$-tree.
$endgroup$
– Kuifje
Dec 4 '18 at 8:48
$begingroup$
In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
$endgroup$
– John Hughes
Dec 4 '18 at 12:22
add a comment |
$begingroup$
Well...it's no longer a tree, so I guess the best I can say is that it's a spanning subgraph. I'm not sure whether your "modifications" always preserve the property that the new graph contains all the vertices. If not, then you can just say "it's a subgraph."
$endgroup$
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
$begingroup$
It is more than a subgraph : it is a $1$-tree.
$endgroup$
– Kuifje
Dec 4 '18 at 8:48
$begingroup$
In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
$endgroup$
– John Hughes
Dec 4 '18 at 12:22
add a comment |
$begingroup$
Well...it's no longer a tree, so I guess the best I can say is that it's a spanning subgraph. I'm not sure whether your "modifications" always preserve the property that the new graph contains all the vertices. If not, then you can just say "it's a subgraph."
$endgroup$
Well...it's no longer a tree, so I guess the best I can say is that it's a spanning subgraph. I'm not sure whether your "modifications" always preserve the property that the new graph contains all the vertices. If not, then you can just say "it's a subgraph."
answered Dec 4 '18 at 2:54
community wiki
John Hughes
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
$begingroup$
It is more than a subgraph : it is a $1$-tree.
$endgroup$
– Kuifje
Dec 4 '18 at 8:48
$begingroup$
In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
$endgroup$
– John Hughes
Dec 4 '18 at 12:22
add a comment |
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
$begingroup$
It is more than a subgraph : it is a $1$-tree.
$endgroup$
– Kuifje
Dec 4 '18 at 8:48
$begingroup$
In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
$endgroup$
– John Hughes
Dec 4 '18 at 12:22
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
$begingroup$
I don't delete the vertices.
$endgroup$
– Nick
Dec 4 '18 at 2:56
$begingroup$
It is more than a subgraph : it is a $1$-tree.
$endgroup$
– Kuifje
Dec 4 '18 at 8:48
$begingroup$
It is more than a subgraph : it is a $1$-tree.
$endgroup$
– Kuifje
Dec 4 '18 at 8:48
$begingroup$
In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
$endgroup$
– John Hughes
Dec 4 '18 at 12:22
$begingroup$
In view of Nick's comment on your answer: I don't think it is a 1-tree. :) It's tough to know without a description of all possible "modifications."
$endgroup$
– John Hughes
Dec 4 '18 at 12:22
add a comment |
$begingroup$
There is a term for this subgraph with a unique cycle: it is a $1$-tree.
Some authors also call it a pseudotree.
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
$endgroup$
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
add a comment |
$begingroup$
There is a term for this subgraph with a unique cycle: it is a $1$-tree.
Some authors also call it a pseudotree.
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
$endgroup$
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
add a comment |
$begingroup$
There is a term for this subgraph with a unique cycle: it is a $1$-tree.
Some authors also call it a pseudotree.
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
$endgroup$
There is a term for this subgraph with a unique cycle: it is a $1$-tree.
Some authors also call it a pseudotree.
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
edited Dec 4 '18 at 8:47
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
answered Dec 4 '18 at 8:40
KuifjeKuifje
7,1552725
7,1552725
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
add a comment |
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
$begingroup$
In my case I can add more than one cycle.
$endgroup$
– Nick
Dec 4 '18 at 10:52
add a comment |
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