Results 1 to 10 of about 908,664 (294)
Vertex degrees of planar graphs [PDF]
Journal of Combinatorial Theory Series B, 1979 AbstractLet G be a planar graph having n vertices with vertex degrees d1, d2,…,dn. It is shown that Σi=1ndi2 ≤ 2n2 + O(n). The main term in this upper bound is best possible.
Cook, R.J
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Random graphs with forbidden vertex degrees [PDF]
Random Structures and Algorithms, 2010 AbstractWe study the random graph Gn,λ/n conditioned on the event that all vertex degrees lie in some given subset $ {\cal S} $ of the nonnegative integers. Subject to a certain hypothesis on $ {\cal S} $, the empirical distribution of the vertex degrees is asymptotically Poisson with some parameter $ \hat{\mu} $ given as the root of a certain ...
Svante Janson
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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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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 ...
Dieter Rautenbach
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Bounding the feedback vertex number of digraphs in terms of vertex degrees
Discrete Applied Mathematics, 2011 The Turan bound is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro-Wei inequality, which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical result. We show how these statements can be generalized to directed
Hermann Gruber
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Some remarks on the sum of powers of the degrees of graphs [PDF]
Transactions on Combinatorics, 2021 Let $G=(V,E)$ be a simple graph with $n\ge 3$ vertices, $m$ edges and vertex degree sequence $\Delta=d_1 \ge d_2 \ge \cdots \ge d_n=\delta>0$. Denote by $S=\{1, 2,\ldots,n\}$ an index set and by $J=\{I=(r_1, r_2,\ldots,r_k) \, | \, 1\le ...
Emina Milovanovic +2 more
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Functions on adjacent vertex degrees of trees with given degree sequence
Open Mathematics, 2014 Wang Hua
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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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Estimation of vertex degrees in a sampled network [PDF]
2017 51st Asilomar Conference on Signals, Systems, and Computers, 2017 The need to produce accurate estimates of vertex degree in a large network, based on observation of a subnetwork, arises in a number of practical settings. We study a formalized version of this problem, wherein the goal is, given a randomly sampled subnetwork from a large parent network, to estimate the actual degree of the sampled nodes.
Apratim Ganguly, Eric D. Kolaczyk
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ON THE DISTRIBUTION OF THE SECOND DEGREES OF CONFIGURATION GRAPHS VERTICES
Transactions of the Karelian Research Centre of the Russian Academy of Sciences, 2019 The object is configuration graphs with N vertices, numbered from 1 to N, whosevertex degrees are independent identically distributed random variables.
Elena Khvorostyanskaya
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