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Third order Randić index of phenylenes

✍ Scribed by Jie Zhang; Hanyuan Deng

Publisher
Springer
Year
2006
Tongue
English
Weight
131 KB
Volume
43
Category
Article
ISSN
0259-9791

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The third-order Randić index of a graph G is defined as , where the summation is taken over all possible paths of length three of G. A recursive formula for computing the third-order Randić index of a hexagonal chain is given in this paper, and the hexagonal chains with the extremal third-order Ran

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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