Frequently, when referring to the edges of an undirected graph $G=(V,E)$, I want to write that $E \subset V \times V$, which isn't correct since the Cartesian product is ordered and the edges are not.

This motivates my question: is there a common notation for a product of sets $A$ and $B$ defined by $\{ \{a,b\} ~|~ a \in A ,~ b \in B \}$?

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    $\begingroup$ $[X]^2$ is used to refer to the set of unordered pairs from a set $X$ (and $[X]^n$ for $n$-tuples). $\endgroup$ – universalset Dec 5 '13 at 15:56
  • $\begingroup$ Per the modified Question, if $A$ and $B$ are disjoint, then the distinction between ordered and unordered pairs is without essential substance. Given an unordered pair, $\{a,b\}$ we can identify the corresponding ordered pair $(a,b)$ by virtue of $A\cap B = \emptyset$. $\endgroup$ – hardmath Dec 5 '13 at 16:16
  • $\begingroup$ @hardmath what part of my question implies disjointness? $\endgroup$ – Austin Buchanan Dec 5 '13 at 16:23
  • $\begingroup$ I'm not trying to put words in your mouth; you do not imply disjointness. I'm merely pointing out a reason that one often avoids the "messiness" of saying $C = \{ \{a,b\} \mid a \in A, b \in B \}$. $\endgroup$ – hardmath Dec 5 '13 at 16:31
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    $\begingroup$ See also: math.stackexchange.com/questions/112935/… $\endgroup$ – Vincent Labatut Nov 6 '17 at 9:54

I use $E \subseteq \binom{V}{2}$. Although, I have seen it used elsewhere, it's probably not a standard notation.

  • $\begingroup$ This notation is often used in graph theory. $\endgroup$ – Frunobulax Sep 14 '14 at 16:57
  • $\begingroup$ This strikes me as awkward in general though because binomial coefficients generally mean "without replacement" $\endgroup$ – Sheridan Grant Jun 24 at 2:57
  • $\begingroup$ @SheridanGrant $\binom{V}{2} = \{X \subseteq V : |X| = 2\}$. Is this not without replacement? $\endgroup$ – user76284 Oct 27 at 20:29
  • $\begingroup$ @user76284 no recollection of this comment but I appear to be a doofus, you're right $\endgroup$ – Sheridan Grant Oct 28 at 22:29

We used $\bar{\times}$ (but without the gap between the bar and the times symbol) in the algebraic graph theory lectures I've attended some years ago. I liked it, however I don't know how common it is.

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    $\begingroup$ FYI, it's not common at all (at least I've never seen it anywhere). Maybe in some fields, but certainly not in all of mathematics. $\endgroup$ – Najib Idrissi Sep 14 '14 at 17:18

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