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.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 7, 8, 22, 25, 66, 73, 204, 231, 513, 576, 1520, 1715, 3763, 4085

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• A. A. Dobrynin (dobr(AT)math.nsc.ru), Distance of iterated line graphs, Graph Theory Notes of NY, 37 (1999), 8-9.

Links

• A. A. Dobrynin and L. S. Mel'nikov, Some results on the Wiener index of iterated line graphs, Electronic Notes in Discrete Mathematics 22 (2005), 469-475
• Index entries for sequences related to trees

Programs

Sage

# needs the package nauty
def a(n):
    c = 0
    for el in graphs.nauty_geng(str(n) + ' -c ' + str(n-1)+':' + str(n-1)):
        g = (el.line_graph()).line_graph()
        if el.wiener_index() == g.wiener_index():
            c+=1
    return c
# Jernej Azarija, Aug 13 2012

Extensions

More terms (from Dobrynin/Mel'nikov reference), Jernej Azarija, Aug 13 2012