Importance: Medium ✭✭
Author(s): Graham, Ronald L.
Keywords: reconstruction
Recomm. for undergrads: no
Posted by: mdevos
on: March 18th, 2007
Problem   for every graph $ G $, we let $ L(G) $ denote the line graph of $ G $. Given that $ G $ is a tree, can we determine it from the integer sequence $ |V(G)|, |V(L(G))|, |V(L(L(G)))|, \ldots $?

Graph reconstruction is a notoriously difficult subject. This conjecture is an unusual type of reconstruction problem where our class of graphs is very limited - just trees, but we are also given relatively little information - just a sequence of integers.


[GR] C. Godsil and G. Royle, Algebraic graph theory. Graduate Texts in Mathematics, 207. Springer-Verlag, New York, 2001 (page 18).

* indicates original appearance(s) of problem.


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