I'm trying to find out whether the following graph has a name: Let $W$ be an $n$-dimensional vector space over $GF(q)$. The vertices of the graph are all the subspaces of $W$. Two subspaces $W_1$ and $W_2$ are connected iff both $|\dim(W_1)-\dim(W_2)|=1$, and either $W_1\subset W_2$ or $W_2\subset W_1$. This is the Hasse diagram of subspace inclusion. I was wondering whether this graph already has a name I can refer to.


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    $\begingroup$ What is wrong with calling it the Hasse diagram of the inclusion poset? $\endgroup$ May 15, 2013 at 15:05
  • $\begingroup$ A quasi-related digraph I am also looking for a reference to in the literature: cstheory.stackexchange.com/questions/17326/name-this-digraph Inclusion digraphs are extremely helpful in a lot of domains when it comes to software testing. You just have to test a minimum dominating set instead of the entire graph. $\endgroup$ May 15, 2013 at 15:18
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    $\begingroup$ There's nothing wrong with it. It's only in the interest of giving due credit that I'm trying to see whether this graph already has a name. $\endgroup$ May 15, 2013 at 15:36
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    $\begingroup$ I don't think it has an actual name (like Grassman graph etc) but I've often heard it referred to vaguely (and ambiguously) as things like "the incidence graph on subspaces" or even "the lattice of subspaces". $\endgroup$ May 16, 2013 at 12:41


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