Let ?$G$? be a graph. Denote by ?$L^i(G)$? 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 ?$i \ge 3$? such that ?$W(L^i(T)) = W(T)$?? In a series of five papers we solve this problem. In a previous paper we proved that ?$W(L^i(T)) > W(T)$? for every tree ?$T$? that is not homeomorphic to a path, claw ?$K_{1,3}$? and to the graph of "letter ?$H$?", where ?$i \ge 3$?. Here we prove that ?$W(L^i(T)) > W(T)$? for every tree ?$T$? homeomorphic to the claw, ?$T \ne K_{1,3}$? and ?$i \ge 4$?.

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URN

URN:NBN:SI:DOC-44IRC9KA

COBISSID

16472921

Added

16.12.2021

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Citation

APA:

Knor, Martin, Potočnik, Primož, Škrekovski, Riste (2013). Wiener index of iterated line graphs of trees homeomorphic to the claw K sub {1,3}. Ars mathematica contemporanea, volume 6, issue 2, str. 211-219. URN:NBN:SI:DOC-44IRC9KA from http://www.dlib.si

MLA:

Knor, Martin, Potočnik, Primož, Škrekovski, Riste. "Wiener index of iterated line graphs of trees homeomorphic to the claw K sub {1,3}." Ars mathematica contemporanea volume 6. issue 2 (2013) str. 211-219.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-44IRC9KA>

Ars mathematica contemporanea
2008-
(Assembly record)