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On the Maximum Atom-Bond Sum-Connectivity Index of Trees

MATCH – Communications in Mathematical and in Computer Chemistry, 2023
Topological indices have been under study since 1947 when H. Wiener proposed a mathematical formula to order the boiling temperatures of isomers of alkanes. Since then, over 3000 similar mathematical formulae have been defined and studied by mathematicians, chemists and by other scientists.
Hu, Yarong, Wang, Fangxia
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Multiplicative Atom Bond Sum Connectivity Index of Certain Nanotubes

Annals of Pure and Applied Mathematics, 2023
We put forward the multiplicative atom bond sum connectivity index of a graph. We determine the atom bond sum connectivity index and the multiplicative atom bond sum connectivity index for some chemical nanostructures such as armchair polyhex nanotubes, zigzag polyhex nanotubes and carbon nanocone networks.
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A Variant of Atom Bond Sum Connectivity Index

Match Communications in Mathematical and in Computer Chemistry
Summary: Topological index is a numerical graph invariant derived from molecular graph. The atom bond sum connectivity index drew a lot of interest from chemical graph theorists in a short period of time. Nowadays, the degree sum of a vertex's first neighbors is recognized as a useful parameter in chemical graph theory. Keeping these two facts in mind,
Yasin H, Mohammed, M, Suresh, Mondal, Sourav   +2 more
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Extremal Results and Bounds for Atom-Bond Sum-Connectivity Index

Match Communications in Mathematical and in Computer Chemistry
The ABS (atom-bond sum-connectivity) index is a topological index, that was introduced in 2022 by amalgamating the main ideas of two well-examined indices. Mathematical aspects (especially, extremal results and bounds) of the ABS index have already been studied considerably.
Akbar Ali, Ivan Gutman, Boris Furtula, Izudin Redžepović, Tomislav Došlić, Zahid Raza   +5 more
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Bounds for the Atom-Bond Sum-Connectivity Index of Graphs

Match Communications in Mathematical and in Computer Chemistry
Summary: The \textit{atom-bond sum-connectivity} \((ABSC)\) index of a graph \(G\) is defined as \(ABSC(G)=\sum\limits_{uv\in E(G)}\sqrt\frac{d_u +d_v -2}{d_u +d_v}\), where \(d_u\) and \(d_v\) represent the degrees of \(u\) and \(v\) in \(G\), respectively.
Hussain, Zaryab, Liu, Hechao, Hua, Hongbo   +2 more
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Maximum Atom Bond Sum Connectivity Index of Molecular Trees with a Perfect Matching

Match Communications in Mathematical and in Computer Chemistry
Summary: \textit{A. Ali} et al. [J. Math. Chem. 60, No. 10, 2081--2093 (2022; Zbl 1498.05065)] introduced a new type of vertex-degree-based topological indices of a graph which is called as atom-bond sum-connectivity (ABS) index. For a graph \(G=(V(G), E(G))\), the ABS index of \(G\) is defined as \[ ABS(G) = \sum_{uv\in E(G)}\sqrt{1 - \frac{2}{d_G(u) +
Wang, Fangxia, Zhang, Yaoyao, Ren, Xiangyu, Zhang, Bo   +3 more
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Maximum Atom-Bond Sum-Connectivity Index in Unicyclic Graphs of Fixed Girth

Match Communications in Mathematical and in Computer Chemistry
Summary: The \(ABS\) (atom-bond sum-connectivity) index of a graph \(G\) is given by the formula: \[ ABS(G) = \sum\limits_{xy\in E(G)} \sqrt{\dfrac{d_x+d_y -2}{d_x +d_y}}, \] where \(d_x\) denotes the degree of vertex \(x\) in the graph \(G\). The primary objective of this research paper is to identify the maximum, and second-maximum \(ABS\) index ...
Nithya, Palaniyappan, Elumalai, Suresh, Balachandran, Selvaraj, Liu, Hechao   +3 more
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The greatest values for atom-bond sum-connectivity index of graphs with given parameters

Discrete Applied Mathematics
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Fengwei Li, Qingfang Ye, Huajing Lu
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On trees of a fixed maximum degree with extremal general atom-bond sum-connectivity index

Journal of Applied Mathematics and Computing
We consider general atom-bond sum-connectivity indices $ABS_l(G)$ for $1/2 \leq l \leq 1$ and study their values over all trees on a given number of vertices with a fixed maximum degree $\Delta $. We obtain both the minimum and the maximum values and characterize the corresponding trees.
Akbar Ali, Tomislav Došlić, Zahid Raza
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Extremal values of the atom-bond sum-connectivity index in bicyclic graphs

Journal of Applied Mathematics and Computing, 2023
Kannan Aarthi, Suresh Elumalai, Selvaraj Balachandran, Sourav Mondal   +3 more
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