# Notation for unordered product of sets

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 $\{ \{a,b\} ~|~ a \in A ,~ b \in B \}$?

• $[X]^2$ is used to refer to the set of unordered pairs from a set $X$ (and $[X]^n$ for $n$-tuples). Dec 5, 2013 at 15:56
• 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 $A\cap B = \emptyset$. Dec 5, 2013 at 16:16
• @hardmath what part of my question implies disjointness? Dec 5, 2013 at 16:23
• 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 $C = \{ \{a,b\} \mid a \in A, b \in B \}$. Dec 5, 2013 at 16:31
• Nov 6, 2017 at 9:54

I use $E \subseteq \binom{V}{2}$. Although, I have seen it used elsewhere, it's probably not a standard notation.
• @SheridanGrant $\binom{V}{2} = \{X \subseteq V : |X| = 2\}$. Is this not without replacement? Oct 27, 2019 at 20:29
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.