Is there a math term for a modificated minimum spanning tree?












0














I have found a minimum spanning tree (left figure).
Then I have applied some modification:




  1. The edge A-B (red) was added,

  2. The edge C-D (green) was rewritten to C'-D.


Edit. I don't delete the vertices.




  1. 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)?




enter image description here










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    0














    I have found a minimum spanning tree (left figure).
    Then I have applied some modification:




    1. The edge A-B (red) was added,

    2. The edge C-D (green) was rewritten to C'-D.


    Edit. I don't delete the vertices.




    1. 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)?




    enter image description here










    share|cite|improve this question



























      0












      0








      0







      I have found a minimum spanning tree (left figure).
      Then I have applied some modification:




      1. The edge A-B (red) was added,

      2. The edge C-D (green) was rewritten to C'-D.


      Edit. I don't delete the vertices.




      1. 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)?




      enter image description here










      share|cite|improve this question















      I have found a minimum spanning tree (left figure).
      Then I have applied some modification:




      1. The edge A-B (red) was added,

      2. The edge C-D (green) was rewritten to C'-D.


      Edit. I don't delete the vertices.




      1. 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)?




      enter image description here







      graph-theory notation terminology






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      edited Dec 4 '18 at 15:35

























      asked Dec 4 '18 at 2:47









      Nick

      301112




      301112






















          2 Answers
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          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."






          share|cite|improve this answer























          • I don't delete the vertices.
            – Nick
            Dec 4 '18 at 2:56










          • It is more than a subgraph : it is a $1$-tree.
            – Kuifje
            Dec 4 '18 at 8:48










          • 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."
            – John Hughes
            Dec 4 '18 at 12:22



















          0














          There is a term for this subgraph with a unique cycle: it is a $1$-tree.



          Some authors also call it a pseudotree.






          share|cite|improve this answer























          • In my case I can add more than one cycle.
            – Nick
            Dec 4 '18 at 10:52











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          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          2














          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."






          share|cite|improve this answer























          • I don't delete the vertices.
            – Nick
            Dec 4 '18 at 2:56










          • It is more than a subgraph : it is a $1$-tree.
            – Kuifje
            Dec 4 '18 at 8:48










          • 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."
            – John Hughes
            Dec 4 '18 at 12:22
















          2














          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."






          share|cite|improve this answer























          • I don't delete the vertices.
            – Nick
            Dec 4 '18 at 2:56










          • It is more than a subgraph : it is a $1$-tree.
            – Kuifje
            Dec 4 '18 at 8:48










          • 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."
            – John Hughes
            Dec 4 '18 at 12:22














          2












          2








          2






          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."






          share|cite|improve this answer














          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."







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          answered Dec 4 '18 at 2:54


























          community wiki





          John Hughes













          • I don't delete the vertices.
            – Nick
            Dec 4 '18 at 2:56










          • It is more than a subgraph : it is a $1$-tree.
            – Kuifje
            Dec 4 '18 at 8:48










          • 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."
            – John Hughes
            Dec 4 '18 at 12:22


















          • I don't delete the vertices.
            – Nick
            Dec 4 '18 at 2:56










          • It is more than a subgraph : it is a $1$-tree.
            – Kuifje
            Dec 4 '18 at 8:48










          • 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."
            – John Hughes
            Dec 4 '18 at 12:22
















          I don't delete the vertices.
          – Nick
          Dec 4 '18 at 2:56




          I don't delete the vertices.
          – Nick
          Dec 4 '18 at 2:56












          It is more than a subgraph : it is a $1$-tree.
          – Kuifje
          Dec 4 '18 at 8:48




          It is more than a subgraph : it is a $1$-tree.
          – Kuifje
          Dec 4 '18 at 8:48












          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."
          – John Hughes
          Dec 4 '18 at 12:22




          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."
          – John Hughes
          Dec 4 '18 at 12:22











          0














          There is a term for this subgraph with a unique cycle: it is a $1$-tree.



          Some authors also call it a pseudotree.






          share|cite|improve this answer























          • In my case I can add more than one cycle.
            – Nick
            Dec 4 '18 at 10:52
















          0














          There is a term for this subgraph with a unique cycle: it is a $1$-tree.



          Some authors also call it a pseudotree.






          share|cite|improve this answer























          • In my case I can add more than one cycle.
            – Nick
            Dec 4 '18 at 10:52














          0












          0








          0






          There is a term for this subgraph with a unique cycle: it is a $1$-tree.



          Some authors also call it a pseudotree.






          share|cite|improve this answer














          There is a term for this subgraph with a unique cycle: it is a $1$-tree.



          Some authors also call it a pseudotree.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 4 '18 at 8:47

























          answered Dec 4 '18 at 8:40









          Kuifje

          7,1082725




          7,1082725












          • In my case I can add more than one cycle.
            – Nick
            Dec 4 '18 at 10:52


















          • In my case I can add more than one cycle.
            – Nick
            Dec 4 '18 at 10:52
















          In my case I can add more than one cycle.
          – Nick
          Dec 4 '18 at 10:52




          In my case I can add more than one cycle.
          – Nick
          Dec 4 '18 at 10:52


















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