4,691 research outputs found

    Degree based Topological indices of Hanoi Graph

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    International audienceThere are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, and so forth are used to characterize the chemical compound. In this paper we computed the edge version of atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, geometric-arithmetic index and fifth geometric-arithmetic index of Double-wheel graph and Hanoi graph. The results are analyzed and the general formulas are derived for the above mentioned families of graphs

    Fourth ABC Index and Fifth GA Index of Certain Special Molecular Graphs

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    Several chemical indices have been introduced in theoretical chemistry to measure the properties of molecular structures, such as atom bond connectivity index and geometric-arithmetic index. In this paper, we present the fourth atom bond connectivity index and fifth geometric-arithmetic index of fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs

    The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

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    Let G=(V,E) be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights ((du+dv−2)/dudv)1/2 over all edges uv of G, where du denotes the degree of a vertex u of G. In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound on the atom-bond connectivity index of catacondensed polyomino graphs with h squares and determine the corresponding extremal graphs

    Topological indices of Sierpiński Gasket and Sierpiński Gasket Rhombus graphs

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    Sierpiński graphs S(n, k) were defined originally in 1997 by Sandi Klavžar and Uroš Milutinović. In this paper atom bond connectivity index, fourth atom bond connectivity indices, geometric arithmetic index, fifth geometric arithmetic indices, augmented Zagreb index and sankruti index of Sierpiński Gasket graphs and Sierpiński Gasket Rhombus graphs are determined.The first author is supported by University Grants Commission, Government of India, for the financial support under the Basic Science Research Fellowship.UGC vide No.F.25 − 1/2014 − 15(BSR)/7 − 349/2012(BSR), January 2015.The Second author is partially supported by the University Grants Commission for financial assistance under No.F.510/12/DRS-II/2018(SAP-I).Publisher's Versio

    On the Difference of Atom-Bond Sum-Connectivity and Atom-Bond-Connectivity Indices

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    The atom-bond-connectivity (ABC) index is one of the well-investigated degree-based topological indices. The atom-bond sum-connectivity (ABS) index is a modified version of the ABC index, which was introduced recently. The primary goal of the present paper is to investigate the difference between the aforementioned two indices, namely ABSABCABS-ABC. It is shown that the difference ABSABCABS-ABC is positive for all graphs of minimum degree at least 22 as well as for all line graphs of those graphs of order at least 55 that are different from the path and cycle graphs. By means of computer search, the difference ABSABCABS-ABC is also calculated for all trees of order at most 1515.Comment: 16 pages and 5 figure

    Atom-bond-connectivity index of certain graphs

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    The ABC index is one of the most applicable topological graph indices and several properties of it has been studied already due to its extensive chemical applications. Several variants of it have also been defined and used for several reasons. In this paper, we calculate the atom-bond connectivity index of some derived graphs such as double graphs, subdivision graphs and complements of some standard graphs.Publisher's Versio

    More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index

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    The first geometric-arithmetic (GA) index and atom-bond connectivity (ABC) index are molecular structure descriptors which play a significant role in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. Das and Trinajsti\'{c} [\textit{Chem. Phys. Lett.} \textbf{497} (2010) 149-151] showed that GAGA index is greater than ABCABC index for all those graphs (except K1,4K_{1,4} and TT^{*}, see Figure 1) in which the difference between maximum and minimum degree is less than or equal to 3. In this note, it is proved that GAGA index is greater than ABCABC index for line graphs of molecular graphs, for general graphs in which the difference between maximum and minimum degree is less than or equal to (2δ1)2(2\delta-1)^{2} (where δ\delta is the minimum degree and δ2\delta\geq2) and for some families of trees. Thereby, a partial solution to an open problem proposed by Das and Trinajsti\'{c} is given.Comment: 10 pages, 2 tables, 1 figure, revised versio

    Atom bond connectivity index of molecular graphs of alkenes and cycloalkenes

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    The atom-bond connectivity (ABC) index is one of the recently most investigated degree based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as ABC(G) = ∑ uv∈E(G) √[d v + du – 2]/[d v · d u ], where du denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkenes and cycloalkenes
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