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Relation between Randić index and average distance of treesCygan, Marek ; Pilipczuk, Michał ; Škrekovski, RisteThe Randić index ▫$R(G)$▫ of a graph ▫$G$▫ is the sum of weights ▫$(\deg(u) \deg(v))^{-0.5}$▫ over all edges ▫$uv$▫ of ▫$G$▫, where ▫$\deg(v)$▫ denotes the degree of a vertex ▫$v$▫. We prove that for ... any tree ▫$T$▫ with ▫$n_1$▫ leaves ▫$R(T) \ge {\rm ad}(T) + \max(0, \sqrt{n_1}-2)$▫, where ▫${\rm ad}(T)$▫ is the average distance between vertices of ▫$T$▫. As a consequence we resolve the conjecture ▫$R(G) \ge {\rm ad}(G)$▫ given by Fajtlowicz in 1988 for the case when ▫$G$▫ is a tree.Source: Match : communications in mathematical and in computer chemistry. - ISSN 0340-6253 (Vol. 66, no. 2, 2011, str. 605-612)Type of material - article, component partPublish date - 2011Language - englishCOBISS.SI-ID - 16589401
Author
Cygan, Marek |
Pilipczuk, Michał |
Škrekovski, Riste
Topics
teorija grafov |
topološki indeks |
Randićev indeks |
drevo |
povprečna razdalja |
graph theory |
topological index |
Randić index |
tree |
average distance
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source: Match : communications in mathematical and in computer chemistry. - ISSN 0340-6253 (Vol. 66, no. 2, 2011, str. 605-612)
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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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Cygan, Marek | ![]() |
Pilipczuk, Michał | ![]() |
Škrekovski, Riste | 15518 |
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