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Vertex degree weighted path indices
Acta Chimica Slovenica, 2015 Vertex degree weighted path indices PN(a, b, ...), for example P1(a, b), P2(a, b, c), P3(a, b, c, d), and P4(a, b, c, d, e), are good topological indices for some of the physicochemical properties of octanes with |R|max up to 0.999.
Anton Perdih
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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 vertex-degree based invariants of digraphs [PDF]
Discrete Mathematics Letters, 2021 Let $D=(V,A)$ be a digraphs without isolated vertices. A vertex-degree based invariant $I(D)$ related to a real function $φ$ of $D$ is defined as a summation over all arcs, $I(D) = \frac{1}{2}\sum_{uv\in A}{φ(d_u^+,d_v^-)}$, where $d_u^+$ (resp. $d_u^-$) denotes the out-degree (resp. in-degree) of a vertex $u$.
Hanyuan Deng +4 more
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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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Alexandria Engineering Journal, 2022 The transition metal is a planar metallic organic structure, and tetra-cyano-benzene is one of the most studied networks of 3D series of transition metal.
Nida Zahra, Muhammad Ibrahim
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THE DEGREE ON CHAIN OF FUZZY GRAPHS
Tikrit Journal of Pure Science, 2023 In this paper, we discussed some types of degrees on chains of fuzzy graphs. also introduced a new type of degree, which is called an average degree.
Russel H. Majeed, Nabeel E. Arif
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Subdomination in Graphs with Upper-Bounded Vertex Degree
Mathematics, 2023 We find a lower bound for the k-subdomination number on the set of graphs with a given upper bound for vertex degrees. We study the cases where the proposed lower bound is sharp, construct the optimal graphs and indicate the corresponding k-subdominating
Darya Lemtyuzhnikova +4 more
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Toughness and Vertex Degrees [PDF]
Journal of Graph Theory, 2012 AbstractWe study theorems giving sufficient conditions on the vertex degrees of a graph G to guarantee G is t‐tough. We first give a best monotone theorem when , but then show that for any integer , a best monotone theorem for requires at least nonredundant conditions, where grows superpolynomially as .
Bauer, D. +4 more
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Vertex degrees close to the average degree
Discrete Mathematics, 2023 Let $G$ be a finite, simple, and undirected graph of order $n$ and average degree $d$. Up to terms of smaller order, we characterize the minimal intervals $I$ containing $d$ that are guaranteed to contain some vertex degree. In particular, for $d_+\in \left(\sqrt{dn},n-1\right]$, we show the existence of a vertex in $G$ of degree between $d_+-\left ...
Pardey, Johannes, Rautenbach, Dieter
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PREFERENTIAL ATTACHMENT WITH FITNESS DEPENDENT CHOICE
Физико-химические аспекты изучения кластеров, наноструктур и наноматериалов, 2021 We study the asymptotic behavior of the maximum degree in the preferential attachment tree model with a choice based on both the degree and fitness of a vertex.
Y.A. Malyshkin
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