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Multiplicative Atom Bond Sum Connectivity Index of Certain Nanotubes
Annals of Pure and Applied Mathematics, 2023We 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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Bounds for the Atom-Bond Sum-Connectivity Index of Graphs
Match Communications in Mathematical and in Computer ChemistrySummary: 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 +2 more
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Extremal Results and Bounds for Atom-Bond Sum-Connectivity Index
Match Communications in Mathematical and in Computer ChemistryThe 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 +5 more
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Maximum Atom Bond Sum Connectivity Index of Cacti
The atom-bond sum-connectivity (ABS) index of a graph is a variant of several well-known chemical topological indices, such as the randi´c index, the sum-connectivity index and the atom-bond connectivity index. For a graph G = (V (G), E(G)), the ABS index of G is defined as <div>   ...Fangxia Wang +3 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 ChemistrySummary: \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 +3 more
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Minimizing the General Atom-Bond Sum-Connectivity Index of Unicyclic Graphs
Journal of applied mathematics and computing. International journalThis paper gives the characterization of those graphs that minimize the general atom- bond sum-connectivity index ABS ȷ among all fixed-order unicyclic graphs of a given maximum degree for 1 ≤ ȷ < 2. It is also proved that the cycle graph uniquely minimizes the aforementioned index in the class of all fixed-order unicyclic graphs.
Akbar Ali +4 more
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Maximum Atom-Bond Sum-Connectivity Index in Unicyclic Graphs of Fixed Girth
Match Communications in Mathematical and in Computer ChemistrySummary: 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 +3 more
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The maximum atom-bond connectivity index for graphs with edge-connectivity one
Discrete Applied Mathematics, 2017Qing Cui, Lingping Zhong
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Maximum values of atom–bond connectivity index in the class of tricyclic graphs
Journal of Applied Mathematics and Computing, 2015Ali Reza Ashrafi, Ashrafi A R
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