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Comparison between the zeroth-order Randić index and the sum-connectivity index

Published: 01 February 2016 Publication History

Abstract

The zeroth-order Randić index and the sum-connectivity index are very popular topological indices in mathematical chemistry. These two indices are based on vertex degrees of graphs and attracted a lot of attention in recent years. Recently Li and Li (2015) studied these two indices for trees of order n. In this paper we obtain a relation between the zeroth-order Randić index and the sum-connectivity index for graphs. From this we infer an upper bound for the sum-connectivity index of graphs. Moreover, we prove that the zeroth-order Randić index is greater than the sum-connectivity index for trees. Finally, we show that R2, α(G) is greater or equal R1, α(G) (α 1) for any graph and characterize the extremal graphs.

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Cited By

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  • (2017)On the general sum-connectivity index of trees with given number of pendent verticesDiscrete Applied Mathematics10.1016/j.dam.2017.01.016222:C(213-221)Online publication date: 11-May-2017
  • (2017)The general Randić index of trees with given number of pendent verticesApplied Mathematics and Computation10.1016/j.amc.2017.01.021302:C(111-121)Online publication date: 1-Jun-2017
  1. Comparison between the zeroth-order Randić index and the sum-connectivity index

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        Published In

        cover image Applied Mathematics and Computation
        Applied Mathematics and Computation  Volume 274, Issue C
        February 2016
        800 pages

        Publisher

        Elsevier Science Inc.

        United States

        Publication History

        Published: 01 February 2016

        Author Tags

        1. Molecular graph
        2. Sum-connectivity index
        3. Zeroth-order Randić index

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        • (2017)On the general sum-connectivity index of trees with given number of pendent verticesDiscrete Applied Mathematics10.1016/j.dam.2017.01.016222:C(213-221)Online publication date: 11-May-2017
        • (2017)The general Randić index of trees with given number of pendent verticesApplied Mathematics and Computation10.1016/j.amc.2017.01.021302:C(111-121)Online publication date: 1-Jun-2017

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