کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
419509 683825 2010 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Which generalized Randić indices are suitable measures of molecular branching?
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Which generalized Randić indices are suitable measures of molecular branching?
چکیده انگلیسی

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 Randić index Rp(G)=∑uv∈E(G)(dudv)pRp(G)=∑uv∈E(G)(dudv)p is a suitable measure for branching if and only if p∈[λ,0)∪(0,λ′)p∈[λ,0)∪(0,λ′) where λλ is the solution of the equation 2x+6x+12⋅12x+14⋅16x−114⋅4x=0 in the interval (−0.793,−0.792)(−0.793,−0.792) and λ′λ′ is the positive solution of the equation 3⋅3x−2⋅2x−4x=03⋅3x−2⋅2x−4x=0. These results include the solution of the problem proposed by Clark and Gutman.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 158, Issue 18, 28 November 2010, Pages 2056–2065
نویسندگان
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