2
$\begingroup$

Do you know a good common term for the operation of connecting a new vertex v to every vertex in a graph G (or a term for such vertex v)?

The ones I know give me poor search results:

  • a nice word for v would be an apex vertex, but this usually only applies for planar G
  • the operation is the join of G and a single vertex graph
  • I have seen v called a complete vertex.
$\endgroup$
1
  • 1
    $\begingroup$ The analogous operation in topology is also called the join in general, and in this particular case is called the cone. $\endgroup$ Feb 5, 2015 at 9:19

2 Answers 2

3
$\begingroup$

The name I've usually seen for such a vertex is "universal vertex".

$\endgroup$
3
  • 3
    $\begingroup$ I've seen the term "dominating vertex" used, but probably prefer universal vertex. $\endgroup$ Feb 5, 2015 at 22:41
  • $\begingroup$ Interesting Gordon. As you can imagine though Gordon, I prefer dominating vertex! Then, that concept I'm very familiar with! $\endgroup$ Feb 6, 2015 at 3:33
  • $\begingroup$ That's (universal) the term I see most often and use myself --- but I have only picked it up somewhere a few years back. $\endgroup$ Feb 7, 2015 at 3:30
2
$\begingroup$

I've always called this operation taking the cone of a graph but I don't recall where I got that terminology from.

$\endgroup$
2
  • 3
    $\begingroup$ I do too. Must have picked it up from you. But I think the moral is that whatever you use, it will have to be defined. $\endgroup$ Feb 6, 2015 at 3:14
  • 1
    $\begingroup$ I think this expression comes from the polytope world... at least this is where I first heard it, and there it is used with abundance. $\endgroup$ Feb 7, 2015 at 3:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.