On the randic index of graphs

Cita com:
hdl:2117/126594
Document typeArticle
Defense date2019-10-01
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Abstract
For a given graph G = (V, E), the degree mean rate of an edge uv ¿ E is a half of the quotient between the geometric and arithmetic means of its end-vertex degrees d(u) and d(v). In this note, we derive tight bounds for the Randic index of G in terms of its maximum and minimum degree mean rates over its edges. As a consequence, we prove the known conjecture that the average distance is bounded above by the Randic index for graphs with
order n large enough, when the minimum degree d is greater than (approximately) ¿1/3 , where ¿ is the maximum degree. As a by-product, this proves that almost all random (Erdos–Rényi) graphs satisfy the conjecture
Description
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitationDalfo, C. On the randic index of graphs. "Discrete mathematics", 11 Setembre 2018, vol. 342, núm. 10, p. 2792-2796.
ISSN0012-365X
Publisher versionhttps://www.sciencedirect.com/science/article/pii/S0012365X18302784
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