The generalized Randić index of trees
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Paul Balister; Béla Bollobás; Stefanie Gerke
📂
Article
📅
2007
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John Wiley and Sons
🌐
English
⚖ 241 KB
## 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