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首页> 外文期刊>Discrete Applied Mathematics >Which generalized Randi? indices are suitable measures of molecular branching?
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Which generalized Randi? indices are suitable measures of molecular branching?

机译：哪个广义的兰迪？指数是分子分支的合适度量？

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Molecular branching is a very important notion, because it influences many physicochemical properties of chemical compounds. However, there is no consensus on how to measure branching. Nevertheless two requirements seem to be obvious: star is the most branched graph and path is the least branched graph. Every measure of branching should have these two graphs as extremal graphs. In this paper we restrict our attention to chemical trees (i.e. simple connected graphs with maximal degree at most 4), hence we have only one requirement that the path be an extremal graph. Here, we show that the generalized Randi? index Rp(G)=∑uv∈E(G)(dudv)p is a suitable measure for branching if and only if p∈[λ,0)∪(0,λ′) where λ is the solution of the equation 2~x+6~x+12·12~x+14· 16~x-114·4~x=0 in the interval (-0.793,-0.792) and λ′ is the positive solution of the equation 3·3 ~x-2·2~x-4x=0. These results include the solution of the problem proposed by Clark and Gutman.
机译：分子分支是一个非常重要的概念，因为它会影响化合物的许多物理化学性质。但是，关于如何测量分支还没有共识。但是，似乎有两个要求很明显：星形是最分支的图，路径是最小分支的图。每个分支度量都应将这两个图作为极值图。在本文中，我们将注意力集中在化学树上（即最大程度最大为4的简单连接图），因此我们仅要求路径为极值图。在这里，我们证明了广义Randi？当且仅当p∈[λ，0）∪（0，λ'）时，Rp（G）= ∑uv∈E（G）（dudv）p才是分支的合适度量，其中λ是方程2的解在区间（-0.793，-0.792）中〜x + 6〜x + 12·12〜x + 14·16〜x-114·4〜x = 0，λ'是等式3·3〜的正解x-2·2〜x-4x = 0。这些结果包括Clark和Gutman提出的问题的解决方案。

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