# What kind of solid has a face adjacency graph whose spanning trees are not feasible nets

Was reading an introductory graph theory book, and it says that nets of solids can be represented using adjacency graphs, and new nets can be discovered by searching for all the spanning trees of the graph.

It also mentions that for some solids known as non-manifold, the spanning trees might not result in feasible nets. It does not elaborate.

I have tried searching this on the internet but it seems quite obscure and all I got were discussions about 3D graphic renderers

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Does the book give definitions of feasible net and non-manifold solid? –  Rahul Jan 11 '13 at 18:32

It is hart to say without the definitions, but it probably refers to the principle behind the following example. Consider two tretrahedra, which are glued at common vertex $v$. I would consider this solid as non-manifold. Any spanning tree has to contain $v$, hence if you cut your solid open at the spanning tree, the "net" is disconnected. And this is probably meant by infeasible.