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  • Wiener index of iterated line graphs of trees homeomorphic to the claw ▫$K_{1,3}$▫
    Knor, Martin ; Potočnik, Primož, 1971- ; Škrekovski, Riste
    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 ▫$i \ge 4$▫.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 6, no. 2, 2013, str. 211-219)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 16472921

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 6, no. 2, 2013, str. 211-219)

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