Randić index and the diameter of a graph

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10102945" target="_blank" >RIV/00216208:11320/11:10102945 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ejc.2010.12.002" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2010.12.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2010.12.002" target="_blank" >10.1016/j.ejc.2010.12.002</a>

Result language
angličtina
Original language name
Randić index and the diameter of a graph
Original language description
The Randic index R(G) of a nontrivial connected graph G is defined as the sum of the weights (d(u)d(v))^(-0.5) over all edges e=uv of G. We prove that R(G) }= d(G)/2, where d(G) is the diameter of G. This immediately implies that R(G) }= r(G)/2, which isthe closest result to the well-known Graffiti conjecture R(G)}= r(G) - 1 of Fajtlowicz, where r(G) is the radius of G. Asymptotically, our result approaches the bound R(G)/d(G) }= (n-3+2*sqrt(2))/(2n-2) conjectured by Aouchiche, Hansen and Zheng.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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