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A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with Zn [version 1; peer review: 2 approved] [PDF]
F1000ResearchBackground The study of algebraic structures through graph-theoretic representations provides a powerful visual and combinatorial framework for analyzing ring-theoretic properties. The ideal-based non-zero divisor graph ∅ I ( Z n ) , constructed from the
Ali Abd Aubad, Sameer Kadem
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Degree-Based Graph Entropy in Structure–Property Modeling
Entropy, 2023 Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose dG(vi) is degree of the vertex vi for each i=1,2,…,n.
Sourav Mondal, Kinkar Chandra Das
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Extremal graphs for vertex-degree-based invariants with given degree sequences [PDF]
Discrete Applied Mathematics, 2019 For a symmetric bivariable function $f(x,y)$, let the {\it connectivity function} of a connected graph $G$ be $M_f(G)=\sum_{uv\in E(G)}f(d(u),d(v))$, where $d(u)$ is the degree of vertex $u$. In this paper, we prove that for an escalating (de-escalating) function $f(x,y)$, there exists a BFS-graph with the maximum (minimum) connectivity function $M_f(G)
Muhuo Liu, Kexiang Xu, Xiao-Dong Zhang
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Estimating vertex-degree-based energies [PDF]
Vojnotehnički Glasnik, 2022 Introduction/purpose: In the current literature, several dozens of vertexdegree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated.
Ivan Gutman
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Relating graph energy with vertex-degree-based energies [PDF]
Vojnotehnički Glasnik, 2020 Introduction/purpose: The paper presents numerous vertex-degree-based graph invariants considered in the literature. A matrix can be associated to each of these invariants.
Ivan Gutman
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On the spectral radius of VDB graph matrices
Vojnotehnički Glasnik, 2023 Introduction/purpose: Vertex-degree-based (VDB) graph matrices form a special class of matrices, corresponding to the currently much investigated vertex-degree-based (VDB) graph invariants. Some spectral properties of these matrices are investigated.
Ivan Gutman
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On vertex and edge degree-based topological indices
Vojnotehnički Glasnik, 2023 Introduction/purpose: The entire topological indices (T Ient) are a class of graph invariants depending on the degrees of vertices and edges. Some general properties of these invariants are established.
Ivan Gutman
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Note on the temperature Sombor index
Vojnotehnički Glasnik, 2023 Introduction/purpose: The temperature of a vertex of a graph of the order n is defined as d/(n-d), where d is the vertex degree. The temperature variant of the Sombor index is investigated and several of its properties established. Methods: Combinatorial
Ivan Gutman
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On General Reduced Second Zagreb Index of Graphs
Mathematics, 2022 Graph-based molecular structure descriptors (often called “topological indices”) are useful for modeling the physical and chemical properties of molecules, designing pharmacologically active compounds, detecting environmentally hazardous substances, etc.
Lkhagva Buyantogtokh +2 more
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The Generalised Colouring Numbers on Classes of Bounded Expansion [PDF]
, 2016 The generalised colouring numbers $\mathrm{adm}_r(G)$, $\mathrm{col}_r(G)$, and $\mathrm{wcol}_r(G)$ were introduced by Kierstead and Yang as generalisations of the usual colouring number, also known as the degeneracy of a graph, and have since then ...
Kreutzer, Stephan +3 more
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