Wiener index of iterated line graphs of trees homeomorphic to the claw K1,3

Martin Knor, Primož Potočnik, Riste Škrekovski

Abstract


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, TK1,3 and i ≥ 4.

Keywords


Wiener index, iterated line graph, tree, claw

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DOI: https://doi.org/10.26493/1855-3974.250.d49

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications