Exact Formula and Improved Bounds for General Sum-Connectivity Index of Graph-Operations

• Main Authors: Maqsood Ahmad, Muhammad Saeed, Muhammad Javaid, Muhammad Hussain
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: Molecular graphs; topological indices; Cartesian product; total graph; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">F</italic>-sum graphs
• Online Access: https://ieeexplore.ieee.org/document/8897501/

For a molecular graph &#x0393;, the general sum-connectivity index is defined as &#x03C7;_&#x03B2;(&#x0393;) = <b>&#x03A3;</b>_{vw&#x2208;E(&#x0393;)}[d_&#x0393;(v) + d_&#x0393;(w)]^&#x03B2;, where &#x03B2; &#x2208; R and d_&#x0393;(v) denotes the degree of the vertex v in the molecular graph &#x0393;. The problem of finding best possible upper and lower bound for certain topological index is of fundamental nature in extremal graph theory. Akhtar and Imran [J. Inequal. Appl. (2016) 241] obtained the sharp bounds of general sum-connectivity index for four graph operations (F-sum graphs) introduced by Eliasi and Taeri [Discrete Appl. Math. 157: 794-803, 2009)]. In this paper, for &#x03B2; &#x2208; N, we figured out and improved the sharp bounds of the general sum-connectivity index for F-sum graphs, where F &#x2208; {R, Q, T}. Several examples are presented to elaborate and compare the results of improved bounds with existing sharp bounds. In addition, we obtained exact formula of general sum-connectivity index for F-sum graphs, when F = S.