Results 11 to 20 of about 193,774 (278)
On the general sum-connectivity index and general Randić index of cacti [PDF]
Journal of Inequalities and Applications, 2016 Let G be a connected graph. The degree of a vertex x of G, denoted by d G ( x ) $d_{G}(x)$ , is the number of edges adjacent to x. The general sum-connectivity index is the sum of the weights ( d G ( x ) + d G ( y ) ) α $(d_{G}(x)+d_{G}(y))^{\alpha}$ for
Shehnaz Akhter +2 more
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On the general sum-connectivity index of hypergraphs
AIMS MathematicsGiven a non-zero real number $ \alpha $, the general sum-connectivity index $ \chi_{\alpha} $ for graph $ G $ is given by the sum $ \Sigma_{xy\in {E(G)}} (d_x+d_y)^{\alpha} $. Here, $ d_x $ denotes the degree of a vertex $ x $ in graph $ G $, and $ E(G) $
Hongzhuan Wang, Piaoyang Yin, Yan Li
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AKCE International Journal of Graphs and Combinatorics, 2017 The general sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graphs of subdivision graphs of tadpole graphs, wheels and ladders have been reported in the literature.
Harishchandra S. Ramane +2 more
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Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs [PDF]
Complexity, 2021 In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs.
Rui Cheng +5 more
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General sum-connectivity index and general Randić index of trees with given maximum degree [PDF]
Discrete Mathematics Letters, 2023 Summary: For trees with given number of vertices \(n\) and maximum degree \(\Delta\), we present lower bounds on the general sum-connectivity index \(\chi_a\) if \(a >0\) and \(3 \leq \Delta \leq n -1\), and an upper bound on the general Randić index \(R_a\) if \(-0.283\leq a
Elize Swartz, Tomáš Vetrík
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Exact Formula and Improved Bounds for General Sum-Connectivity Index of Graph-Operations
IEEE Access, 2019 For a molecular graph Γ, the general sum-connectivity index is defined as χβ(Γ) = Σvw∈E(Γ)[dΓ(v) + dΓ(w)]β, where β ∈ R and dΓ(v) denotes the degree of the vertex ...
Maqsood Ahmad +3 more
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On the Minimal General Sum-Connectivity Index of Connected Graphs Without Pendant Vertices [PDF]
IEEE Access, 2019 The general sum-connectivity index of a graph $G$ , denoted by $\chi _{_\alpha }(G)$ , is defined as $\sum _{uv\in E(G)}(d(u)+d(v))^{\alpha }$ , where $uv$ is the edge connecting the vertices $u,v\in V(G)$ , $d(w)$ denotes the degree of a vertex
Akbar Ali +4 more
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The sharp bounds on general sum-connectivity index of four operations on graphs [PDF]
Journal of Inequalities and Applications, 2016 The general sum-connectivity index χ α ( G ) $\chi_{\alpha}(G)$ , for a (molecular) graph G, is defined as the sum of the weights ( d G ( a 1 ) + d G ( a 2 ) ) α $(d_{G}(a_{1})+d_{G}(a_{2}))^{\alpha}$ of all a 1 a 2 ∈ E ( G ) $a_{1}a_{2}\in E(G)$ , where
Shehnaz Akhter, Muhammad Imran
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On the general sum-connectivity index of connected graphs with given order and girth [PDF]
Electronic Journal of Graph Theory and Applications, 2016 In this paper, we show that in the classof connected graphs $G$ of order $n\geq 3$ having girth at least equal to $k$, $3\leq k\leq n$, the unique graph $G$ having minimum general sum-connectivity index $\chi _{\alpha }(G)$ consists of $C_{k}$ and $n-k ...
Ioan Tomescu
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Two-Matchings with Respect to the General Sum-Connectivity Index of Trees
AxiomsA vertex-degree-based topological index φ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in ...
Roberto Cruz, Mateo Lopez, Juan Rada
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