Results 11 to 20 of about 174,518,636 (296)
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 ...
Johannes Pardey, Dieter Rautenbach
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Scientific Annals of Computer ScienceThe energy of a vertex in a graph plays a very important role in terms of its contribution to the total energy of a graph, a significant graph invariant in the field of chemical graph theory.
P. N. Simha +4 more
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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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Sparse Vertex Cutsets and the Maximum Degree
The Electronic Journal of CombinatoricsWe show that every graph $G$ of maximum degree $\Delta$ and sufficiently large order has a vertex cutset $S$ of order at most $\Delta$ that induces a subgraph $G[S]$ of maximum degree at most $\Delta-3$. For $\Delta\in \{ 4,5\}$, we refine this result by considering also the average degree of $G[S]$.
Bessy, Stéphane +3 more
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Distribution of Vertex Degree in Web-Graphs
Combinatorics, Probability and Computing, 2006 We give results for the age-dependent distribution of vertex degree and number of vertices of given degree in the undirected web-graph process, a discrete random graph process introduced in [8]. For such processes we show that as $k \rightarrow \infty$, the expected proportion of vertices of degree $k$ has power law parameter $1+1/\eta$ where $\eta$ is
COLIN COOPER, Cooper, Colin
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On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem [PDF]
, 2018 We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound.
Ordyniak, Sebastian +2 more
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Vertex-degree-based topological indices of uniform directed hypergraphs
Arab Journal of Basic and Applied SciencesModelling a chemical network is crucial for understanding the complex interactions and dynamics within a chemical system, allowing for precise predictions of reaction behaviour under various conditions.
Shashwath S. Shetty, K. Arathi Bhat
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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 .
Douglas Bauer +4 more
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The complexity of degree anonymization by vertex addition [PDF]
Theoretical Computer Science, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robert Bredereck +5 more
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The SLD vertex detector upgrade (VXD3) and a study of bbg events [PDF]
, 1998 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis presents a variety of work concerning the design, construction and use of the SLD's vertex detector.
Dervan, Paul John
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