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RELATION BETWEEN GENERAL RANDIC INDEX AND ´ GENERAL SUM CONNECTIVITY INDEX

South East Asian J. of Mathematics and Mathematical Sciences, 2022
The general Randi´c index is the sum of weights of (d(u).d(v))k for every edge uv of a molecular graph G. On the other hand general Sum-Connectivity index is the sum of the weights (d(u) + d(v))k for every edge uv of G, where k is a real number and d(u) is the degree of vertex u.
V. S., Shigehalli, Dsouza, Austin Merwin
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On General Sum-Connectivity Index of Trees of Fixed Maximum Degree and Order

Match Communications in Mathematical and in Computer Chemistry, 2022
Summary: The general sum-connectivity index is a molecular descriptor introduced within the field of mathematical chemistry about a decade ago. For an arbitrary real number \(\alpha\), the general sum-connectivity index of a graph \(G\) is denoted \(\chi_{\alpha}(G)\) and is defined as the sum of the numbers \(\left(d(u) + d(v)\right)^{\alpha}\) over ...
Raza, Zahid, Balachandran, Selvaraj, Elumalai, Suresh, Ali, Akbar   +3 more
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On the general sum-connectivity index of tricyclic graphs

Journal of Applied Mathematics and Computing, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhongxun Zhu
exaly   +2 more sources

General sum-connectivity index of unicyclic graphs with given diameter and girth

Discrete Mathematics, Algorithms and Applications, 2021
Topological indices of graphs have been studied due to their extensive applications in chemistry. We obtain lower bounds on the general sum-connectivity index [Formula: see text] for unicyclic graphs [Formula: see text] of given girth and diameter, and for unicyclic graphs of given diameter, where [Formula: see text].
T. Vetrík
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Minimum general sum-connectivity index of unicyclic graphs

Journal of Mathematical Chemistry, 2010
The general sum-connectivity index of a graph G is defined as X alpha(G) = Sigma edges (d(u) + d(v))(alpha), where d(u) denotes the degree of vertex u in G and a is alpha real number. In this report, we determine the minimum and the second minimum values of the general sum-connectivity indices of n-vertex unicyclic graphs for non-zero alpha >= -1, and ...
Zhibin Du, Bo Zhou, Nenad Trinajstić
exaly   +2 more sources

Two-tree graphs with maximum general sum-connectivity index

Discrete Mathematics, Algorithms and Applications, 2020
For a simple graph [Formula: see text], the general sum-connectivity index is defined as [Formula: see text], where [Formula: see text] is the degree of the vertex [Formula: see text] and [Formula: see text] is a real number. In this paper, we will obtain sharp upper bounds on the general sum-connectivity index for [Formula: see text].
R. Khoeilar, H. Shooshtari
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General sum-connectivity index of unicyclic graphs with given maximum degree

Discrete Applied Mathematics
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Elize Swartz, Tomás Vetrík
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A Note on the General Sum–Connectivity Index of a Graph and Its Line Graph

Match Communications in Mathematical and in Computer Chemistry
Summary: For a real number \(\beta\), the general sum-connectivity index \(\chi_\beta(G)\) of a graph \(G\) is defined as \(\chi_\beta(G) = \sum_{xy\in E(G)}(d_G(x) + d_G(y))^\beta\), where \(d(x)\) denote the degree of a vertex \(x\) in \(G\). In Chen (2023), the author present the lower bounds for \(\chi_\beta(L(G))\) in terms of \(\chi_\beta(G ...
Su, Zhenhua, Tang, Zikai, Chen, Shubo
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The Minimum General Sum-Connectivity Index of Trees with Given Matching Number

Bulletin of the Malaysian Mathematical Sciences Society, 2019
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Lingping Zhong
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Progress in general sum-connectivity index

2011 International Conference on Electronics, Communications and Control (ICECC), 2011
The general sum-connectivity index of a graph G is defined as χ a (G) = Σ uv∊E(G) (d u +d v )α, where d u (or d v ) denotes the degree of vertex u (or v) in G, E(G) denotes the edge set of G, and α is a real number. This paper outlines the results up to now on this problem.
Peng Shuying
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