Sep 3, 2010 · I was wondering about a couple of graph enumeration issues. First, is it possible to enumerate all simple graphs with a given degree sequence?
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We consider the estimation of the number of labelled simple graphs with degree sequence d1, d2, . . . , dn by using an n-dimensional Cauchy integral.
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. As a ...
Our goal is to compute the number of isomorphism classes of graphs with a given degree sequence. Let G be a graph of order p. Define r(G)<S, as ~EI'(G) iff a ...
We survey results on counting graphs with given degree sequence, focusing on asymptotic results, and mentioning some of the applications of these results. The ...
Jan 6, 2021 · We show that the exact number of labeled graphs that realize a fixed degree sequence satisfies a simple recurrence relation.
We determine the asymptotic number of labelled graphs with a given degree sequence for the case where the maximum degree is o(IE(G)I1/3).
The method used is a switching argument recently used by us to uniformly generate random graphs with given degree sequences.
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. As a ...
Jun 29, 2020 · We provide asymptotic formulae for the numbers of bipartite graphs with given degree sequence, and of loopless digraphs with given in- and out-degree sequences.