cp's OEIS Frontend

A051175 Number of trees T of order n such that W(T) = W(L(L(T))) where W(G) and L(G) are the Wiener index and line graph of a graph G.

%I A051175 #23 Feb 28 2021 18:52:39
%S A051175 0,0,0,0,0,0,0,0,1,1,1,0,7,8,22,25,66,73,204,231,513,576,1520,1715,
%T A051175 3763,4085
%N A051175 Number of trees T of order n such that W(T) = W(L(L(T))) where W(G) and L(G) are the Wiener index and line graph of a graph G.
%D A051175 A. A. Dobrynin (dobr(AT)math.nsc.ru), Distance of iterated line graphs, Graph Theory Notes of NY, 37 (1999), 8-9.
%H A051175 A. A. Dobrynin and L. S. Mel'nikov, <a href="https://doi.org/10.1016/j.endm.2005.06.081">Some results on the Wiener index of iterated line graphs</a>, Electronic Notes in Discrete Mathematics 22 (2005), 469-475
%H A051175 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%o A051175 (Sage) # needs the package nauty
%o A051175 def a(n):
%o A051175     c = 0
%o A051175     for el in graphs.nauty_geng(str(n) + ' -c ' + str(n-1)+':' + str(n-1)):
%o A051175         g = (el.line_graph()).line_graph()
%o A051175         if el.wiener_index() == g.wiener_index():
%o A051175             c+=1
%o A051175     return c
%o A051175 # _Jernej Azarija_, Aug 13 2012
%K A051175 nonn
%O A051175 1,13
%A A051175 _N. J. A. Sloane_
%E A051175 More terms (from Dobrynin/Mel'nikov reference), _Jernej Azarija_, Aug 13 2012