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.
Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ The analogous operation in topology is also called the join in general, and in this particular case is called the cone. $\endgroup$
    – Qiaochu Yuan
    Commented Feb 5, 2015 at 9:19

2 Answers 2

Reset to default
3
$\begingroup$

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

Improve this answer
$\endgroup$
3
  • 3
    $\begingroup$ I've seen the term "dominating vertex" used, but probably prefer universal vertex. $\endgroup$
    – Gordon Royle
    Commented 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! $\endgroup$
    – Paul Burchett
    Commented 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. $\endgroup$
    – Flo Pfender
    Commented 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.

Improve this answer
$\endgroup$
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. $\endgroup$
    – Chris Godsil
    Commented 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. $\endgroup$
    – Flo Pfender
    Commented Feb 7, 2015 at 3:28

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .