The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees

Li, Jing; Li, Yiyang

doi:10.1016/j.amc.2015.06.028

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…where α ∈ R \ {0}. There have been numerous contributions in the chemical and mathematical literature published on the general product-connectivity index, see, for example, [2,[22][23][24][25].…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons

Hayat,

Arfan,

Khan

et al. 2024

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For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=∑xy∈EGϕ(dx,dy), where ϕ is a symmetric map and di is the degree of i∈VG. For α∈R, if ϕ=(dxdy)α (resp. ϕ=(dx+dy)α), the index is called the general product-connectivity Rα (resp. general sum-connectivity SCIα) index. In this paper, by formulating an optimization problem, we determine the value(s) of α, for which the linear/multiple correlation coefficient of Rα and SCIα with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area.

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Section: Mathematical Preliminariesmentioning

confidence: 99%

An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons

Hayat,

Arfan,

Khan

et al. 2024

Axioms

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“…a quantity conceived already in 1976 [50], but which was examined only in a relatively small number of subsequent papers (see e.g., [51][52][53]). Most results on M…”

Section: Special Casesmentioning

confidence: 99%

Beyond the Zagreb indices

Gutman

Milovanovic²,

Milovanovic³

2020

AKCE International Journal of Graphs and Combinatorics

108

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The two Zagreb indices M 1 = ∑ v d(v) 2 and M 2 = ∑ uv d(u) d(v) are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a variety of modifications of M 1 and M 2 were put forward. The present survey of these modified Zagreb indices outlines their main mathematical properties, and provides an exhaustive bibliography.

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Comparison between the zeroth-order Randić index and the sum-connectivity index

Das

Dehmer

2016

Applied Mathematics and Computation

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The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees

Cited by 6 publications

References 14 publications

An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons

An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons

Beyond the Zagreb indices

Comparison between the zeroth-order Randić index and the sum-connectivity index

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