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November 23

Vertex degree: terminology for d(v) = n-1?

Does anybody know of some term used for a vertex connected to all other vertex, i.e. a vertex with degree n-1? None is listed under Degree (graph theory)#Special cases of degree value.

I was thinking of calling such a vertex "promiscuous", but since I'm not a native English speaker, I wonder if this would be prohibitively silly?

TIA, Phaunt (talk) 10:40, 23 November 2007 (UTC)[reply]

I think your suggestion would be properly "Prominent"... I would call it "Omni-Connected" but I don't know of any actually term being given besides "n-1". A math-wiki (talk) 12:34, 23 November 2007 (UTC)[reply]

Co-isolated was the just thing that came to my mind. I think I've been spending too much time on category theory. Algebraist 13:00, 23 November 2007 (UTC)[reply]

Thank you for your suggestions so far.

Thinking further, hub vertex and star vertex came to mind. The first is the name some authors give to the centre of a wheel graph; the second connotes the star graph (what? a red link? see here), though from a google scholar search, the second term seems to have been used in a different sense already. Searching a thesaurus for antonyms of 'isolated' (from the suggestion of 'co-isolated'), I came up with "sociable", but this may be just as silly as "promiscuous". (It invokes an idea of the vertices in my graphs having a social life which I may not be comfortable with....) Phaunt (talk) 13:58, 23 November 2007 (UTC)[reply]

"Graph center"; not quite, but close. —Preceding unsigned comment added by 84.187.113.101 (talk) 21:46, 23 November 2007 (UTC)[reply]

"Fully connected vertex" is a bit of a mouthful, but should hopefully express the issue without ambiguity. If you want a monosyllable, I kind of like "hub". Just remember to define it clearly. Not that there's IMHO anything wrong with "promiscuous", either — much sillier terms have been used by quite respectable mathematicians. —Ilmari Karonen (talk) 17:00, 24 November 2007 (UTC)[reply]

List of silly mathematical terms – No? How disappointing. —Tamfang (talk) 01:22, 30 December 2007 (UTC)[reply]