set theory definition

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n,m is positive integer satisfying $n \ge m$

An undirected graph $S_{n,m} =(V_{n,m},E_{n,})$ defined as follows:

$V_{n,m}=\{{A|A \, is \, a \,subset \, of \, {1,2...n}}\}$

$E=\{\{{A,B}|A,B \in V_{n,m} $the element contained only in one of A and B exactly m exist$\}$

i need to draw $S_{2,1} , S_{2,3}$

$V=\{\{\},{1},{2},{3},{1,2}\}$

but why i dont understand the definition of edge here? is this mean $A \cup B$?

can someone explain to me?