The maximum Randić index of chemical trees with pendants
✍ Scribed by Wai Chee Shiu; Lian-zhu Zhang
- Book ID
- 108114125
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 836 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract The generalized Randić; index ${R}\_{-\alpha}(T)$ of a tree __T__ is the sum over the edges ${u}{v}$ of __T__ of $(d(u)d(v))^{-\alpha}$ where ${d}(x)$ is the degree of the vertex __x__ in __T__. For all $\alpha > 0$, we find the minimal constant $\beta\_{0}=\beta\_{0}(\alpha)$ such that
The Wiener polarity index W p (G) of a graph G = (V , E) is the number of unordered pairs of vertices {u, v} of G such that the distance d G (u, v) between u and v is 3. In this work, we give the maximum Wiener polarity index of trees with n vertices and k pendants and find that the maximum value is