Distinct Minimum Weight Spanning Trees
$begingroup$
I am trying to find the total number of distinct minimum weight spanning trees(MWST) in a simple, undirected, unlabeled and weighted graph but I am confused whether should I have to consider Isomorphic trees(if it is present) as a single minimum weight spanning tree or not while counting the distinct MWSTs because graph is unlabeled.
For example, If I have a graph as :-
Now, I have to find the Total number of distinct minimum weight spanning trees(MWST) in the above weighted graph.
I got total $3times2 =6 $ possibilities of MWSTs but I also found the possibility of Isomorphic trees in these total $6$ MWSTs because graph is unlabeled. For example,the below $2$ MWSTs are Isomorphic in nature for the above given graph.
Similarly , If I have a simple, weighted, undirected and unlabeled graph as :
Now, I got total $2^{2} times 2^{4} = 64$ MWSTs but If I consider Isomorphism property in a graph then I am getting 2 Isomorphic Trees as :
So, If I consider the possibility of many Isomorphic trees like above in the given graph then total number of distinct MWSTs will be less than $6$ and $64$ in the above 2 cases respectively. But I am not sure whether it is correct or not.
So, My doubt is :- While counting the total number of distinct MWSTs in an unlabeled graph, Should I have to consider Isomorphic MWSTs as a single minimum weight spanning tree or not ?
Please help.
graph-theory algorithms
edited Dec 14 '18 at 23:32
nafhgood
1,805422
asked Dec 14 '18 at 17:53
ankitankit
33
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add a comment |
$begingroup$
I am trying to find the total number of distinct minimum weight spanning trees(MWST) in a simple, undirected, unlabeled and weighted graph but I am confused whether should I have to consider Isomorphic trees(if it is present) as a single minimum weight spanning tree or not while counting the distinct MWSTs because graph is unlabeled.
For example, If I have a graph as :-
Now, I have to find the Total number of distinct minimum weight spanning trees(MWST) in the above weighted graph.
I got total $3times2 =6 $ possibilities of MWSTs but I also found the possibility of Isomorphic trees in these total $6$ MWSTs because graph is unlabeled. For example,the below $2$ MWSTs are Isomorphic in nature for the above given graph.
Similarly , If I have a simple, weighted, undirected and unlabeled graph as :
Now, I got total $2^{2} times 2^{4} = 64$ MWSTs but If I consider Isomorphism property in a graph then I am getting 2 Isomorphic Trees as :
So, If I consider the possibility of many Isomorphic trees like above in the given graph then total number of distinct MWSTs will be less than $6$ and $64$ in the above 2 cases respectively. But I am not sure whether it is correct or not.
So, My doubt is :- While counting the total number of distinct MWSTs in an unlabeled graph, Should I have to consider Isomorphic MWSTs as a single minimum weight spanning tree or not ?
Please help.
graph-theory algorithms
edited Dec 14 '18 at 23:32
nafhgood
1,805422
asked Dec 14 '18 at 17:53
ankitankit
33
$endgroup$
add a comment |
$begingroup$
I am trying to find the total number of distinct minimum weight spanning trees(MWST) in a simple, undirected, unlabeled and weighted graph but I am confused whether should I have to consider Isomorphic trees(if it is present) as a single minimum weight spanning tree or not while counting the distinct MWSTs because graph is unlabeled.
For example, If I have a graph as :-
Now, I have to find the Total number of distinct minimum weight spanning trees(MWST) in the above weighted graph.
I got total $3times2 =6 $ possibilities of MWSTs but I also found the possibility of Isomorphic trees in these total $6$ MWSTs because graph is unlabeled. For example,the below $2$ MWSTs are Isomorphic in nature for the above given graph.
Similarly , If I have a simple, weighted, undirected and unlabeled graph as :
Now, I got total $2^{2} times 2^{4} = 64$ MWSTs but If I consider Isomorphism property in a graph then I am getting 2 Isomorphic Trees as :
So, If I consider the possibility of many Isomorphic trees like above in the given graph then total number of distinct MWSTs will be less than $6$ and $64$ in the above 2 cases respectively. But I am not sure whether it is correct or not.
So, My doubt is :- While counting the total number of distinct MWSTs in an unlabeled graph, Should I have to consider Isomorphic MWSTs as a single minimum weight spanning tree or not ?
Please help.
graph-theory algorithms
edited Dec 14 '18 at 23:32
nafhgood
1,805422
asked Dec 14 '18 at 17:53
ankitankit
33
$endgroup$
I am trying to find the total number of distinct minimum weight spanning trees(MWST) in a simple, undirected, unlabeled and weighted graph but I am confused whether should I have to consider Isomorphic trees(if it is present) as a single minimum weight spanning tree or not while counting the distinct MWSTs because graph is unlabeled.
For example, If I have a graph as :-
Now, I have to find the Total number of distinct minimum weight spanning trees(MWST) in the above weighted graph.
I got total $3times2 =6 $ possibilities of MWSTs but I also found the possibility of Isomorphic trees in these total $6$ MWSTs because graph is unlabeled. For example,the below $2$ MWSTs are Isomorphic in nature for the above given graph.
Similarly , If I have a simple, weighted, undirected and unlabeled graph as :
Now, I got total $2^{2} times 2^{4} = 64$ MWSTs but If I consider Isomorphism property in a graph then I am getting 2 Isomorphic Trees as :
So, If I consider the possibility of many Isomorphic trees like above in the given graph then total number of distinct MWSTs will be less than $6$ and $64$ in the above 2 cases respectively. But I am not sure whether it is correct or not.
So, My doubt is :- While counting the total number of distinct MWSTs in an unlabeled graph, Should I have to consider Isomorphic MWSTs as a single minimum weight spanning tree or not ?
Please help.
graph-theory algorithms
graph-theory algorithms
edited Dec 14 '18 at 23:32
nafhgood
1,805422
asked Dec 14 '18 at 17:53
ankitankit
33
edited Dec 14 '18 at 23:32
nafhgood
1,805422
asked Dec 14 '18 at 17:53
ankitankit
33
edited Dec 14 '18 at 23:32
nafhgood
1,805422
edited Dec 14 '18 at 23:32
nafhgood
1,805422
edited Dec 14 '18 at 23:32
nafhgood
1,805422
1,805422
asked Dec 14 '18 at 17:53
ankitankit
33
asked Dec 14 '18 at 17:53
ankitankit
33
asked Dec 14 '18 at 17:53
ankitankit
33
33
add a comment |
add a comment |
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