796 research outputs found

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

    Get PDF
    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

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

    Full text link
    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

    Comparison Between Zagreb Eccentricity Indices and the Eccentric Connectivity Index, the Second Geometric-arithmetic Index and the Graovac-Ghorbani Index

    Get PDF
    The concept of Zagreb eccentricity indices was introduced in the chemical graph theory very recently. The eccentric connectivity index is a distance-based molecular structure descriptor that was used for mathematical modeling of biological activities of diverse nature. The second geometric-arithmetic index was introduced in 2010, is found to be useful tool in QSPR and QSAR studies. In 2010 Graovac and Ghorbani introduced a distance-based analog of the atom-bond connectivity index, the Graovac-Ghorbani index, which yielded promising results when compared to analogous descriptors. In this note we prove that for chemical trees T. For connected graph G of order n with maximum degree, it is proved that if and, otherwise. Moreover, we show that for paths and some class of bipartite graphs. This work is licensed under a Creative Commons Attribution 4.0 International License
    corecore