XPost: comp.theory, sci.logic, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 29/12/2025 16:08, Richard Damon wrote:   
   > On 12/29/25 10:47 AM, olcott wrote:   
      
   >> I am not going to let you dodge a mandatory prerequisite.   
   >> Your question indicates that you do not know what a   
   >> directed acyclic graph is. A DAG can have a root.   
   >>   
   >   
   > Right, but the thing you say is a DAG doesn't, so can't be a DAG.   
   >   
   > Your problem is you don't understand what the words you are using   
   > actually mean, or the fundamentals of the theory you are trying to talk   
   > about.   
      
   I just flicked through Volume 4A "Combinatorial Algorithms Part 1) of   
   TAOCP (Knuth). Knuth only uses "Root" there, AFAICS, wrt. trees and tree   
   diagrams such as Binary Decision Trees. The DAG doesn't have a "root"   
   defined but the trees that some DAGs and networks on them correspond to   
   do. He doesn't give a definition with properties that we can use to   
   label a node of a DAG as "root" formally.   
      
   I think its fair to allow anyone to call a node the root when being a   
   typical conversationalist when the DAG or a network on it maps to   
   exactly one tree but to allow anyone to say no a DAG has a root. The   
   root of a tree comes with the perspective that it is a tree - which   
   doesn't merely have a unique node with no inarcs but it has a node   
   nominated as a root to make it a tree instead of a mere DAG or a network   
   on a DAG.   
      
   Tree's are usually networks (graphs with data associated). I don't know   
   if, formally, they always are.   
      
      
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   Tristan Wibberley   
      
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