A graph with max 5 nodes that fulfils the folowing requirements
It should contain exactly four cycles and these should all have length 4;
ii) Your graph should contain a node which has degree 3;
iii) Your graph should contain a subgraph which is a tree that has a depth of 3 and
which has two nodes at level 2.
iv) Your graph should contain the smallest number of nodes possible given the
constraints above.
graph-theory
asked Dec 8 at 23:07
DumbellDoor
111
|
show 3 more comments
It should contain exactly four cycles and these should all have length 4;
ii) Your graph should contain a node which has degree 3;
iii) Your graph should contain a subgraph which is a tree that has a depth of 3 and
which has two nodes at level 2.
iv) Your graph should contain the smallest number of nodes possible given the
constraints above.
graph-theory
asked Dec 8 at 23:07
DumbellDoor
111
1
Have you tried anything? Also, I'm having trouble seeing the point of iv, as i and especially iii seems to require the maximum of 5 nodes anyways.
– Arthur
Dec 8 at 23:11
I have tried (a,b) (b,c) (b,d) (b,e) (c,e) (e,b) , but I either get 3 cycles or 6 if I make any more edges and cannot get them to be exactly 4 of length 4.
– DumbellDoor
Dec 8 at 23:14
Are you allowed to have parallel edges?
– mathnoob
Dec 9 at 5:49
What is depth of a tree?
– mathnoob
Dec 9 at 6:04
@mathnoob The depth (or height) of a tree is the maximum depth of any node in the tree; in other words, it is the length of the longest path from the root to any node.
– Alex Ravsky
Dec 9 at 6:37
|
show 3 more comments
It should contain exactly four cycles and these should all have length 4;
ii) Your graph should contain a node which has degree 3;
iii) Your graph should contain a subgraph which is a tree that has a depth of 3 and
which has two nodes at level 2.
iv) Your graph should contain the smallest number of nodes possible given the
constraints above.
graph-theory
asked Dec 8 at 23:07
DumbellDoor
111
It should contain exactly four cycles and these should all have length 4;
ii) Your graph should contain a node which has degree 3;
iii) Your graph should contain a subgraph which is a tree that has a depth of 3 and
which has two nodes at level 2.
iv) Your graph should contain the smallest number of nodes possible given the
constraints above.
graph-theory
graph-theory
asked Dec 8 at 23:07
DumbellDoor
111
asked Dec 8 at 23:07
DumbellDoor
111
asked Dec 8 at 23:07
DumbellDoor
111
asked Dec 8 at 23:07
DumbellDoor
111
asked Dec 8 at 23:07
DumbellDoor
111
111
1
Have you tried anything? Also, I'm having trouble seeing the point of iv, as i and especially iii seems to require the maximum of 5 nodes anyways.
– Arthur
Dec 8 at 23:11
I have tried (a,b) (b,c) (b,d) (b,e) (c,e) (e,b) , but I either get 3 cycles or 6 if I make any more edges and cannot get them to be exactly 4 of length 4.
– DumbellDoor
Dec 8 at 23:14
Are you allowed to have parallel edges?
– mathnoob
Dec 9 at 5:49
What is depth of a tree?
– mathnoob
Dec 9 at 6:04
@mathnoob The depth (or height) of a tree is the maximum depth of any node in the tree; in other words, it is the length of the longest path from the root to any node.
– Alex Ravsky
Dec 9 at 6:37
|
show 3 more comments
1
Have you tried anything? Also, I'm having trouble seeing the point of iv, as i and especially iii seems to require the maximum of 5 nodes anyways.
– Arthur
Dec 8 at 23:11
I have tried (a,b) (b,c) (b,d) (b,e) (c,e) (e,b) , but I either get 3 cycles or 6 if I make any more edges and cannot get them to be exactly 4 of length 4.
– DumbellDoor
Dec 8 at 23:14
Are you allowed to have parallel edges?
– mathnoob
Dec 9 at 5:49
What is depth of a tree?
– mathnoob
Dec 9 at 6:04
@mathnoob The depth (or height) of a tree is the maximum depth of any node in the tree; in other words, it is the length of the longest path from the root to any node.
– Alex Ravsky
Dec 9 at 6:37
1
1
Have you tried anything? Also, I'm having trouble seeing the point of iv, as i and especially iii seems to require the maximum of 5 nodes anyways.
– Arthur
Dec 8 at 23:11
Have you tried anything? Also, I'm having trouble seeing the point of iv, as i and especially iii seems to require the maximum of 5 nodes anyways.
– Arthur
Dec 8 at 23:11
I have tried (a,b) (b,c) (b,d) (b,e) (c,e) (e,b) , but I either get 3 cycles or 6 if I make any more edges and cannot get them to be exactly 4 of length 4.
– DumbellDoor
Dec 8 at 23:14
I have tried (a,b) (b,c) (b,d) (b,e) (c,e) (e,b) , but I either get 3 cycles or 6 if I make any more edges and cannot get them to be exactly 4 of length 4.
– DumbellDoor
Dec 8 at 23:14
Are you allowed to have parallel edges?
– mathnoob
Dec 9 at 5:49
Are you allowed to have parallel edges?
– mathnoob
Dec 9 at 5:49
What is depth of a tree?
– mathnoob
Dec 9 at 6:04
What is depth of a tree?
– mathnoob
Dec 9 at 6:04
@mathnoob The depth (or height) of a tree is the maximum depth of any node in the tree; in other words, it is the length of the longest path from the root to any node.
– Alex Ravsky
Dec 9 at 6:37
@mathnoob The depth (or height) of a tree is the maximum depth of any node in the tree; in other words, it is the length of the longest path from the root to any node.
– Alex Ravsky
Dec 9 at 6:37
|
show 3 more comments
1 Answer
1
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Here is a graph that satisfy the conditions I think:
answered Dec 9 at 13:04
mathnoob
1,786422
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Here is a graph that satisfy the conditions I think:
answered Dec 9 at 13:04
mathnoob
1,786422
add a comment |
Here is a graph that satisfy the conditions I think:
answered Dec 9 at 13:04
mathnoob
1,786422
add a comment |
Here is a graph that satisfy the conditions I think:
answered Dec 9 at 13:04
mathnoob
1,786422
Here is a graph that satisfy the conditions I think:
answered Dec 9 at 13:04
mathnoob
1,786422
answered Dec 9 at 13:04
mathnoob
1,786422
answered Dec 9 at 13:04
mathnoob
1,786422
answered Dec 9 at 13:04
mathnoob
1,786422
1,786422
add a comment |
add a comment |
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1
Have you tried anything? Also, I'm having trouble seeing the point of iv, as i and especially iii seems to require the maximum of 5 nodes anyways.
– Arthur
Dec 8 at 23:11
I have tried (a,b) (b,c) (b,d) (b,e) (c,e) (e,b) , but I either get 3 cycles or 6 if I make any more edges and cannot get them to be exactly 4 of length 4.
– DumbellDoor
Dec 8 at 23:14
Are you allowed to have parallel edges?
– mathnoob
Dec 9 at 5:49
What is depth of a tree?
– mathnoob
Dec 9 at 6:04
@mathnoob The depth (or height) of a tree is the maximum depth of any node in the tree; in other words, it is the length of the longest path from the root to any node.
– Alex Ravsky
Dec 9 at 6:37