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I've recently encountered a problem which heavily involves analysis of structures analogous to weighted trees with no nodes of degree two (such a node along with its adjacent edges would be indistinguishable from a single edge with weight equal to that of said two edges combined). In doing research on the problem, I am hampered by not knowing the structure's proper name. Does such a name exist?

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  • $\begingroup$ The keyterm graph homeomorphism may be of interest, but I've never seen it used to describe weighted graphs. This might be a good question to ask on ComputerScience.SE. $\endgroup$ – Mike Pierce Oct 5 '15 at 4:00
  • $\begingroup$ Thank you for the term, it does seem like it might be useful. The weighting of the graph is incidental to the analysis I need to do. I was hoping that there would be some term like 'smooth', based on the page you linked, to describe such a graph. $\endgroup$ – P... Oct 5 '15 at 4:17
  • $\begingroup$ You could describe your smooth graph to be the "homeomorphic graph of minimum order" (because the smooth graph with no degree-2 vertices would have to have the lowest order of all graphs equivalent under homeomorphism). I don't know if there is already some name for this in the literature, though. $\endgroup$ – Mike Pierce Oct 5 '15 at 4:44
  • $\begingroup$ I recommend asking the question on mathoverflow.com: they often are more familiar with more advanced topics. Though try not to ask too often over there... $\endgroup$ – Alex Mar 4 '16 at 3:18

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