Re: [math-fun] breakthrough in linear algebra
Henry wrote: << . . . Interestingly, _planar graphs_ play a part in this paper! Who knew that linear algebra & planar graphs were connected ? . . .
Actually, any graph G can be defined by its connectivity matrix M = (m_ij), with m_ij = 1 if an edge connects nodes i and j, and 0 if not. Then there is the question of how the invariants of M, like its eigenvalues, are related to topological properties of G. This may not seem very closely fetched, but evidently people have got a lot of mileage out of it. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
When I was an undergraduate at MIT, Gary Miller was working there on rapid algorithms for determining whether graphs were planar. I tried to actually implement one of his algorithms, but at the time my programming chops weren't up to it. If this is the same guy, which seems likely. On Fri, Oct 22, 2010 at 12:10 PM, Daniel Asimov <dasimov@earthlink.net>wrote:
Henry wrote:
<< . . . Interestingly, _planar graphs_ play a part in this paper! Who knew that linear algebra & planar graphs were connected ? . . .
Actually, any graph G can be defined by its connectivity matrix M = (m_ij), with m_ij = 1 if an edge connects nodes i and j, and 0 if not. Then there is the question of how the invariants of M, like its eigenvalues, are related to topological properties of G.
This may not seem very closely fetched, but evidently people have got a lot of mileage out of it.
--Dan
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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Allan Wechsler -
Daniel Asimov