Geodesic
Wiener index of iterated line graphs of trees homeomorphic to the claw K_1,3
Ars Mathematica Contemporanea, Tome 6 (2013) no. 2, pp. 211-219.

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Let G be a graph. Denote by Li(G) its i-iterated line graph and denote by W(G) its Wiener index. Dobrynin, Entringer and Gutman stated the following problem: Does there exist a non-trivial tree T and i ≥ 3 such that W(Li(T)) = W(T)? In a series of five papers we solve this problem. In a previous paper we proved that W(Li(T)) > W(T) for every tree T that is not homeomorphic to a path, claw K1,3 and to the graph of "letter H", where i ≥ 3. Here we prove that W(Li(T)) > W(T) for every tree T homeomorphic to the claw, T ≠ K1,3 and i ≥ 4.
DOI : 10.26493/1855-3974.250.d49
Keywords: Wiener index, iterated line graph, tree, claw 
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Martin Knor; Primož Potočnik; Riste Škrekovski. Wiener index of iterated line graphs of trees homeomorphic to the claw K_1,3. Ars Mathematica Contemporanea, Tome 6 (2013) no. 2, pp. 211-219. doi : 10.26493/1855-3974.250.d49. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.250.d49/

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