[SeqFan]. Adjacency matrix, correction. Was: A possible candidate for OEIS

Antti Karttunen antti.karttunen at gmail.com
Mon Aug 21 19:39:03 CEST 2006


Antti Karttunen wrote:

> Brendan McKay wrote:
>
>> Equivalently, directed graphs (simple but loops allowed) without a
>> few small forbidden subgraphs (those allowing 2 distinct paths of
>> length 2 from vertex x to vertex y for some x,y; I think there are
>> 6 possibilities).  Nice.
>>
>>  
>>
> Nice interpretation! For those SeqFanaticians for whom the above 
> connection seems entirely mysterious,
> please read this: http://mathworld.wolfram.com/AdjacencyMatrix.html
> and it should be clear.

Not at all clear, because the page actually _doesn't mention_ the useful 
property
of an adjacency matrix that an entry a(i,j) in its nth power gives the 
number
of distinct ways to traverse with n steps from vertex i to vertex j.
(And Wikipedia is not any better: 
http://en.wikipedia.org/wiki/Adjacency_matrix )
But this page explains it: http://mathworld.wolfram.com/GraphPower.html

-- Same.








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