Results 1 to 10 of about 3,967,804 (356)

Susceptibility of random graphs with given vertex degrees [PDF]

, 2009
We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process.
Janson, Svante
core   +6 more sources

Vertex degrees close to the average degree [PDF]

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.
Johannes Pardey, D. Rautenbach
semanticscholar   +4 more sources

Monotonicity, asymptotic normality and vertex degrees in random graphs [PDF]

, 2007
We exploit a result by Nerman which shows that conditional limit theorems hold when a certain monotonicity condition is satisfied. Our main result is an application to vertex degrees in random graphs, where we obtain asymptotic normality for the number ...
Janson, Svante
core   +4 more sources

Limit distributions of maximum vertex degree in a conditional configuration graph

Transactions of the Karelian Research Centre of the Russian Academy of Sciences, 2018
We consider configuration graphs with N vertices. The degrees of the vertices are independent identically distributed  random variables following the power-law distribution with positive parameter τ.
Irina Cheplyukova
doaj   +3 more sources

Functions on adjacent vertex degrees of trees with given degree sequence

Open Mathematics, 2014
In this note we consider a discrete symmetric function f(x, y) where $$f(x,a) + f(y,b) \geqslant f(y,a) + f(x,b) for any x \geqslant y and a \geqslant b,$$ associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the
Wang Hua
doaj   +2 more sources

Majorization and the number of bipartite graphs for given vertex degrees [PDF]

Transactions on Combinatorics, 2018
The emph{bipartite realisation problem} asks for a pair of non-negative‎, ‎non-increasing integer lists $a:=(a_1,ldots,a_n)$ and $b:=(b_1,ldots,b_{n'})$ if there is a labeled bipartite graph $G(U,V,E)$ (no loops or multiple edges) such that each vertex ...
Annabell Berger
doaj   +2 more sources

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, Marjan Matejic, Igor Milovanovic   +2 more
doaj   +1 more source

Vertex degrees in grid graphs of permutations [PDF]

Discrete Mathematics Letters
Aubrey Blecher, Arnold Knopfmacher
doaj   +2 more sources

Random graphs with given vertex degrees and switchings [PDF]

Random Struct. Algorithms, 2019
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph.
S. Janson
semanticscholar   +1 more source

Limit laws of planar maps with prescribed vertex degrees [PDF]

Combinatorics, probability & computing, 2018
We prove a generalmulti-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.
Gwendal Collet, M. Drmota, Lukas Daniel Klausner   +2 more
semanticscholar   +1 more source