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How to prove that if we have two DAGs (Directed Acyclic Graph) D1 , D2 and if D1+ = D2+ then (D1)= (D2). D+ means that in this graph there is a positive length path. Example: D grapth may have point A and B, but in D+ graph these two are connected. (D) means that it is a... covering graph,if I got the name right. Example: in graph D there may be point A,B,C and all are interconnected with various paths. in (D) there will be only one path left between each one.

Misho Metreveli
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    Rather than hope that we know what $D!+$ and $(D)$ is, couldn't you take the minute it would have taken you to write it down? Many people on this site (myself included) have not studied enough graph theory to know specific notation, but understand enough to answer many questions anyway. – Arthur Nov 07 '14 at 17:59

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If I'm understanding your notation correctly, it would suffice to show that $(D) = (D+)$, since then $D_1+ = D_2+$ implies $(D_1) = (D_1+) = (D_2+) = (D_2)$. Can you figure out how to show that?

Gregory J. Puleo
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  • The problem is that I don't know how to show that. I understand the idea of proof but can't express it in an acceptable form. I could draw a graph and show an example but I think that it wouldn't suffice as a proof. – Misho Metreveli Nov 07 '14 at 18:14