Graph with at most 2 degrees of separation between every node, but minimal average degree
0
Is there a simple way to construct such a graph? For example a fully connected graph obviously has degree of separation between every node of 1 but has maximal total degree. I can sort of see an algorithm starting with a cycle5 graph and adding nodes until the degree of separation between each pair of nodes is <= 2, but not sure if this would be optimal.
graph-theory
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
add a comment |
0
Is there a simple way to construct such a graph? For example a fully connected graph obviously has degree of separation between every node of 1 but has maximal total degree. I can sort of see an algorithm starting with a cycle5 graph and adding nodes until the degree of separation between each pair of nodes is <= 2, but not sure if this would be optimal.
graph-theory
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
As this question is not a programming question per se, it would be better suited at mathoverflow or the computer science stack exchange.
– Paul Brodersen
Nov 15 '18 at 11:31
Also, if the number of nodes is not constrained to be constant, the answer is a square / triangle / pair of 2 connected nodes. If the number of nodes is given and constant, I think the answer is a star graph.
– Paul Brodersen
Nov 15 '18 at 11:34
Thanks, I realize im actually trying to minimise the average (not total) degree, I was thinking algorithmically about the problem so asked it here, but I will post to mathoverflow.
– ben macintosh
Nov 16 '18 at 3:39
1
I'm voting to close this question as off-topic because it is not a computer programming question (yet).
– Raymond Chen
Nov 16 '18 at 4:47
add a comment |
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Is there a simple way to construct such a graph? For example a fully connected graph obviously has degree of separation between every node of 1 but has maximal total degree. I can sort of see an algorithm starting with a cycle5 graph and adding nodes until the degree of separation between each pair of nodes is <= 2, but not sure if this would be optimal.
graph-theory
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
Is there a simple way to construct such a graph? For example a fully connected graph obviously has degree of separation between every node of 1 but has maximal total degree. I can sort of see an algorithm starting with a cycle5 graph and adding nodes until the degree of separation between each pair of nodes is <= 2, but not sure if this would be optimal.
graph-theory
graph-theory
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
edited Nov 16 '18 at 3:39
ben macintosh
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
asked Nov 15 '18 at 0:18
ben macintoshben macintosh
112
112
As this question is not a programming question per se, it would be better suited at mathoverflow or the computer science stack exchange.
– Paul Brodersen
Nov 15 '18 at 11:31
Also, if the number of nodes is not constrained to be constant, the answer is a square / triangle / pair of 2 connected nodes. If the number of nodes is given and constant, I think the answer is a star graph.
– Paul Brodersen
Nov 15 '18 at 11:34
Thanks, I realize im actually trying to minimise the average (not total) degree, I was thinking algorithmically about the problem so asked it here, but I will post to mathoverflow.
– ben macintosh
Nov 16 '18 at 3:39
1
I'm voting to close this question as off-topic because it is not a computer programming question (yet).
– Raymond Chen
Nov 16 '18 at 4:47
add a comment |
As this question is not a programming question per se, it would be better suited at mathoverflow or the computer science stack exchange.
– Paul Brodersen
Nov 15 '18 at 11:31
Also, if the number of nodes is not constrained to be constant, the answer is a square / triangle / pair of 2 connected nodes. If the number of nodes is given and constant, I think the answer is a star graph.
– Paul Brodersen
Nov 15 '18 at 11:34
Thanks, I realize im actually trying to minimise the average (not total) degree, I was thinking algorithmically about the problem so asked it here, but I will post to mathoverflow.
– ben macintosh
Nov 16 '18 at 3:39
1
I'm voting to close this question as off-topic because it is not a computer programming question (yet).
– Raymond Chen
Nov 16 '18 at 4:47
As this question is not a programming question per se, it would be better suited at mathoverflow or the computer science stack exchange.
– Paul Brodersen
Nov 15 '18 at 11:31
As this question is not a programming question per se, it would be better suited at mathoverflow or the computer science stack exchange.
– Paul Brodersen
Nov 15 '18 at 11:31
Also, if the number of nodes is not constrained to be constant, the answer is a square / triangle / pair of 2 connected nodes. If the number of nodes is given and constant, I think the answer is a star graph.
– Paul Brodersen
Nov 15 '18 at 11:34
Also, if the number of nodes is not constrained to be constant, the answer is a square / triangle / pair of 2 connected nodes. If the number of nodes is given and constant, I think the answer is a star graph.
– Paul Brodersen
Nov 15 '18 at 11:34
Thanks, I realize im actually trying to minimise the average (not total) degree, I was thinking algorithmically about the problem so asked it here, but I will post to mathoverflow.
– ben macintosh
Nov 16 '18 at 3:39
Thanks, I realize im actually trying to minimise the average (not total) degree, I was thinking algorithmically about the problem so asked it here, but I will post to mathoverflow.
– ben macintosh
Nov 16 '18 at 3:39
1
1
I'm voting to close this question as off-topic because it is not a computer programming question (yet).
– Raymond Chen
Nov 16 '18 at 4:47
I'm voting to close this question as off-topic because it is not a computer programming question (yet).
– Raymond Chen
Nov 16 '18 at 4:47
add a comment |
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As this question is not a programming question per se, it would be better suited at mathoverflow or the computer science stack exchange.
– Paul Brodersen
Nov 15 '18 at 11:31
Also, if the number of nodes is not constrained to be constant, the answer is a square / triangle / pair of 2 connected nodes. If the number of nodes is given and constant, I think the answer is a star graph.
– Paul Brodersen
Nov 15 '18 at 11:34
Thanks, I realize im actually trying to minimise the average (not total) degree, I was thinking algorithmically about the problem so asked it here, but I will post to mathoverflow.
– ben macintosh
Nov 16 '18 at 3:39
1
I'm voting to close this question as off-topic because it is not a computer programming question (yet).
– Raymond Chen
Nov 16 '18 at 4:47