Results 1 to 10 of about 21,234 (294)
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 ...
Geoffrey Grimmett, Svante Janson
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Vertex degrees of planar graphs
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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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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Component Order Edge Connectivity, Vertex Degrees, and Integer Partitions
Theory and Applications of GraphsGiven a finite, simple graph G, the k-component order connectivity (resp. edge connectivity) of G is the minimum number of vertices (resp. edges) whose removal results in a subgraph in which every component has an order of at most k − 1.
Michael R. Yatauro
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On the degrees of a strongly vertex-magic graph
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Camino Balbuena +8 more
core +3 more sources
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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, 2016 We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers D. Our results rely on a classical bijection with mobiles (objects exhibiting a tree structure), combined with ...
Collet, Gwendal +2 more
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Bridge and cycle degrees of vertices of graphs [PDF]
International Journal of Mathematics and Mathematical Sciences, 1984 The bridge degree bdeg v and cycle degree cdeg v of a vertex v in a graph G are, respectively, the number of bridges and number of cycle edges incident with v in G. A characterization of finite nonempty sets S of nonnegative integers is given for which S
Gary Chartrand +2 more
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Theta expansion of first massive vertex operator in pure spinor
Journal of High Energy Physics, 2018 We provide the covariant superspace equations that are sufficient to determine the complete θ expansion of the vertex operator of the open string massive states with (mass)2 = 1/α′ in pure spinor formalism of superstring theory.
Subhroneel Chakrabarti +2 more
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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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