Results 241 to 250 of about 193,960 (258)

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].
Khoeilar, R., Shooshtari, H.
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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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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.
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Extremal Values of the General Harmonic Index and General Sum-Connectivity Index of f-Benzenoids

Polycyclic Aromatic Compounds, 2020
The general harmonic index and general sum-connectivity index are two degree-based topological indices which reflect certain structural features of organic molecules.
Qingfang Ye, Fengwei Li, Ruixuan Ye
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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].
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On the General Sum–Connectivity Co–Index of Graphs

2011
In this paper, a new molecular-structure descriptor, the general sum–connectivity co–index   is considered, which generalizes the first Zagreb co–index and the general sum– connectivity index of graph theory. We mainly explore the lower and upper bounds in terms of the order and size for this new invariant.
SU, G., XU, L.
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On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes

2010
The general sum-connectivity index of a graph G, denoted by ) (G a a χ χ = is defined as ∑ ∈ + = ) ( ) ( G E uv a v u a d d χ , where du (or dv) is the degree of the vertex u (or v). Efficient formulas for calculating the general sum-connectivity index of benzenoid systems and their phenylenes are given, and a relation is established between the ...
CHEN, SH., XIA, F., YANG, J.
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General Sum-Connectivity Index with a = 1 for Trees and Unicyclic Graphs with k Pendants

2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2015
One of the newest molecular descriptors, the general sum-connectivity index of a graph G is defined as ?a(G) = Suv?E(G)(d(u)+d(v))a, where d(u) denotes the degree of vertex u in G and a is a real number. The aim of this paper is to determine the trees and the unicyclic graphs with k pendant vertices that maximize the general sum-connectivity index for ...
Rozica-Maria Tache, Ioan Tomescu
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General ( α , 2 ) Path Sum Connectivity Index of Nanostructures

Journal of Corrosion and Materials
The general path sum connectivity index of a molecular graph, denoted as t χ α ( G ) , is defined for a graph G , where α is a positive real number and t is a positive integer. This index is expressed as: t χ α ( G ) = ∑ p t = v j 1 v j 2 … v j t + 1 ⊆ G [ d G ( v j 1 ) + d G ( v j 2 ) + ⋯ + d G ( v j t + 1 ) ] α , where p t represents a ...
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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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