Further results on computation of topological indices of certain networks
01 Sep 2017-Iet Control Theory and Applications (The Institution of Engineering and Technology)-Vol. 11, Iss: 13, pp 2065-2071
TL;DR: In this article, the sum-connectivity index and multiplicative Zagreb indices for certain networks of chemical importance such as silicate networks, hexagonal networks, oxide networks, and honeycomb networks were computed.
Abstract: There are various topological indices such as degree based topological indices, distance based topological indices and counting related topological indices etc. These topological indices correlate certain physicochemical properties such as boiling point, stability of chemical compounds. In this study, the authors compute the sum-connectivity index and multiplicative Zagreb indices for certain networks of chemical importance such as silicate networks, hexagonal networks, oxide networks, and honeycomb networks. Moreover, a comparative study using computer-based graphs has been made to clarify their nature for these families of networks.
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TL;DR: The computational complexity of the Hosoya index of a given graph is known to be NP-complete as discussed by the authors, where RT(G) is the graph constructed from R (G) by a triangle instead of all vertices of the initial graph G.
Abstract: The computational complexity of the Hosoya index of a given graph is NP-Complete. Let RT(G) be the graph constructed from R(G) by a triangle instead of all vertices of the initial graph G. In this ...
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31 citations
TL;DR: This work explores the multiplicative Zagreb indices of bipartite graphs of order n with diameter d, and sharp upper bounds are obtained for these indices of graphs in B ( n, d ) , where B is the set of all n -vertex bipartites graphs with the diameter d.
31 citations
Cites background from "Further results on computation of t..."
...Many researchers are attracted by the idea of finding bounds for graph invariants and the related problem of figuring out the graphs achieving the maximum and minimum values of corresponding indices [3, 4, 5, 6]....
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TL;DR: In this article, the distance-based topological descriptors of chemical networks have been studied for the first time, including the Mostar index, Szeged index, PI index, index, and index.
Abstract: Structure-based topological descriptors of chemical networks enable us the prediction of physico-chemical properties and the bioactivities of compounds through QSAR/QSPR methods. Topological indices are the numerical values to represent a graph which characterises the graph. One of the latest distance-based topological index is the Mostar index. In this paper, we study the Mostar index, Szeged index, PI index, index, and index, for chain oxide network , chain silicate network , ortho chain , and para chain , for the first time. Moreover, analytically closed formulae for these structures are determined.
21 citations
01 Oct 2018
TL;DR: A comparative study using computer-based graphs has been carried out first time to clarify the nature of the computed topological descriptors for the probabilistic neural networks.
Abstract: Abstract A topological index is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. In [Javaid and Cao, Neural Computing and Applications, DOI 10.1007/s00521-017-2972-1], the various degree-based topological indices for the probabilistic neural networks are studied. We extend this study by considering the calculations of the other topological indices, and derive the analytical closed formulas for these new topological indices of the probabilistic neural network. Moreover, a comparative study using computer-based graphs has been carried out first time to clarify the nature of the computed topological descriptors for the probabilistic neural networks. Our results extend some known conclusions.
21 citations
Cites background from "Further results on computation of t..."
...More studies about topological indices of other networks, one may refer to [10, 11]....
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References
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TL;DR: In this paper, the structural dependence of the Huckel total φ-electron energy on the molecular topology of conjugated molecules has been studied and general rules governing the structural properties of the φ energy in conjugate molecules have been derived.
1,706 citations
TL;DR: In this paper, a graph-theoretical study of acyclic polyenes is carried out with an emphasis on the influence of branching on several molecular properties, including thermodynamic stability and reactivity.
Abstract: A graph‐theoretical study of acyclic polyenes is carried out with an emphasis on the influence of branching on several molecular properties. A definition of branching is given and several branching indices are analyzed. The case of polyenes without a Kekule structure is discussed briefly. The main conclusions are: (a) thermodynamic stability of conjugated polyenes decreases with branching, but (b) reactivity, in general, increases with branching.
653 citations
TL;DR: In this article, lower and upper bounds in terms of other graph invariants for the general sum-connectivity index were reported. And the Nordhaus-Gaddum-type result for the generalized Zagreb index was given.
Abstract: We report some properties especially lower and upper bounds in terms of other graph invariants for the general sum-connectivity index which generalizes both the ordinary sum-connectivity index and the first Zagreb index. Additionally, we give the Nordhaus-Gaddum-type result for the general sum-connectivity index.
318 citations
"Further results on computation of t..." refers background in this paper
...The properties of ∏∗ 1(G), χα(G) polynomials for some chemical structures have been studied in [8, 41]....
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TL;DR: The hyper-Zagreb index, first multiple Zag Croatia index, second multiple ZAGreb index and Zagreb polynomials for some nanostar dendrimers are determined.
154 citations
TL;DR: The atom-bond connectivity index (ABC index) and geometric–arithmetic index (GA index) for oxide and chain silicate networks are computed in this paper.
149 citations
"Further results on computation of t..." refers background in this paper
...Silicates are obtained by fusing metal oxides or metal carbonates with sand [20], see Figure 2....
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...One of most interesting topics is to obtain the quantitative structure activity/ property/toxicity relationships [5, 6, 20, 30, 32]....
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