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On a conjecture about Wiener index in iterated line graphs of treesKnor, Martin ; Potočnik, Primož, 1971- ; Škrekovski, RisteLet ▫$G$▫ be a graph. Denote by ▫$L^i(G)$▫ its ▫$i$▫-iterated line graph and denote by ▫$W(G)$▫ its Wiener index. Dobrynin and Melnikov conjectured that there exists no nontrivial tree ▫$T$▫ and ... ▫$i\ge 3$▫, such that ▫$W(L^i(T)) = W(T)$▫. We prove this conjecture for trees which are not homeomorphic to the claw ▫$K_{1,3}$▫ and ▫$H$▫, where ▫$H$▫ is a tree consisting of 6 vertices, 2 of which have degree 3.Source: Discrete mathematics. - ISSN 0012-365X (Vol. 312, iss. 6, 2012, str. 1094-1105)Type of material - article, component partPublish date - 2012Language - englishCOBISS.SI-ID - 16161881
Author
Knor, Martin |
Potočnik, Primož, 1971- |
Škrekovski, Riste
Topics
teorija grafov |
Wienerjev indeks |
povezani grafi |
drevo |
graph theory |
Wiener index |
line graphs |
iterated line graphs |
tree
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Knor, Martin | 36238 |
Potočnik, Primož, 1971- | 18838 |
Škrekovski, Riste | 15518 |
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