Graphs with $operatorname{diam}(G)=2operatorname{rad}(G)$
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When is the diameter of a graph equal to twice of radius? I am currently studying graph theory and have faced many questions related to graphs with the mentioned property. Is there any general class of graphs which follow this property?
I know path graphs with odd vertices are such graphs, but is there a more general graph?
graph-theory
edited Nov 13 at 10:40
Bernard
115k637108
asked Nov 13 at 9:58
Ankit Kumar
32510
add a comment |
up vote
1
down vote
favorite
When is the diameter of a graph equal to twice of radius? I am currently studying graph theory and have faced many questions related to graphs with the mentioned property. Is there any general class of graphs which follow this property?
I know path graphs with odd vertices are such graphs, but is there a more general graph?
graph-theory
edited Nov 13 at 10:40
Bernard
115k637108
asked Nov 13 at 9:58
Ankit Kumar
32510
1
A tree has this property if and only if it has a center vertex. By a center vertex, I mean, consider iteratively removing leaves, i.e. at step one, remove all leaves, then at step 2 repeat. In a tree, you'll either be left with an edge or with a vertex. If you're left with a vertex, then that's called the center vertex of the tree. You can quickly check that a center vertex of a tree is exactly the realizer that $diam(G)=2rad(G)$.
– munchhausen
Nov 13 at 18:00
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
When is the diameter of a graph equal to twice of radius? I am currently studying graph theory and have faced many questions related to graphs with the mentioned property. Is there any general class of graphs which follow this property?
I know path graphs with odd vertices are such graphs, but is there a more general graph?
graph-theory
edited Nov 13 at 10:40
Bernard
115k637108
asked Nov 13 at 9:58
Ankit Kumar
32510
When is the diameter of a graph equal to twice of radius? I am currently studying graph theory and have faced many questions related to graphs with the mentioned property. Is there any general class of graphs which follow this property?
I know path graphs with odd vertices are such graphs, but is there a more general graph?
graph-theory
graph-theory
edited Nov 13 at 10:40
Bernard
115k637108
asked Nov 13 at 9:58
Ankit Kumar
32510
edited Nov 13 at 10:40
Bernard
115k637108
asked Nov 13 at 9:58
Ankit Kumar
32510
edited Nov 13 at 10:40
Bernard
115k637108
edited Nov 13 at 10:40
Bernard
115k637108
edited Nov 13 at 10:40
Bernard
115k637108
115k637108
asked Nov 13 at 9:58
Ankit Kumar
32510
asked Nov 13 at 9:58
Ankit Kumar
32510
asked Nov 13 at 9:58
Ankit Kumar
32510
32510
1
A tree has this property if and only if it has a center vertex. By a center vertex, I mean, consider iteratively removing leaves, i.e. at step one, remove all leaves, then at step 2 repeat. In a tree, you'll either be left with an edge or with a vertex. If you're left with a vertex, then that's called the center vertex of the tree. You can quickly check that a center vertex of a tree is exactly the realizer that $diam(G)=2rad(G)$.
– munchhausen
Nov 13 at 18:00
add a comment |
1
A tree has this property if and only if it has a center vertex. By a center vertex, I mean, consider iteratively removing leaves, i.e. at step one, remove all leaves, then at step 2 repeat. In a tree, you'll either be left with an edge or with a vertex. If you're left with a vertex, then that's called the center vertex of the tree. You can quickly check that a center vertex of a tree is exactly the realizer that $diam(G)=2rad(G)$.
– munchhausen
Nov 13 at 18:00
1
1
A tree has this property if and only if it has a center vertex. By a center vertex, I mean, consider iteratively removing leaves, i.e. at step one, remove all leaves, then at step 2 repeat. In a tree, you'll either be left with an edge or with a vertex. If you're left with a vertex, then that's called the center vertex of the tree. You can quickly check that a center vertex of a tree is exactly the realizer that $diam(G)=2rad(G)$.
– munchhausen
Nov 13 at 18:00
A tree has this property if and only if it has a center vertex. By a center vertex, I mean, consider iteratively removing leaves, i.e. at step one, remove all leaves, then at step 2 repeat. In a tree, you'll either be left with an edge or with a vertex. If you're left with a vertex, then that's called the center vertex of the tree. You can quickly check that a center vertex of a tree is exactly the realizer that $diam(G)=2rad(G)$.
– munchhausen
Nov 13 at 18:00
add a comment |
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A tree has this property if and only if it has a center vertex. By a center vertex, I mean, consider iteratively removing leaves, i.e. at step one, remove all leaves, then at step 2 repeat. In a tree, you'll either be left with an edge or with a vertex. If you're left with a vertex, then that's called the center vertex of the tree. You can quickly check that a center vertex of a tree is exactly the realizer that $diam(G)=2rad(G)$.
– munchhausen
Nov 13 at 18:00