Asymptotic expansions for enumerating connected labelled graphs
Keith Briggs
TL;DR
This paper derives asymptotic expansions to estimate the number of connected labelled graphs with a given number of nodes and edges, focusing on cases where the number of edges exceeds the number of nodes by a small margin.
Contribution
It provides explicit asymptotic formulas for counting connected labelled graphs, extending previous results to include several terms of the expansion for small edge excess.
Findings
Derived asymptotic formulas for connected labelled graphs
Extended enumeration results to higher-order terms
Applicable for small edge excess scenarios
Abstract
I compute several terms of the asymptotic expansion of the number of connected labelled graphs with n nodes and m edges, for small k=m-n.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Combinatorial Mathematics · Advanced Graph Theory Research