Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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.

Thanks

share|improve this question
7  
What is wrong with calling it the Hasse diagram of the inclusion poset? –  Stephen Sturgeon May 15 '13 at 15:05
    
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. –  Chad Brewbaker May 15 '13 at 15:18
1  
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. –  Moshe Schwartz May 15 '13 at 15:36
2  
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". –  Gordon Royle May 16 '13 at 12:41
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.