Unlabelled ordered DAGs and labelled DAGs: constructive enumeration and uniform random sampling

Directed Acyclic Graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs an omnipresent data structure computer science and the problem of counting given number vertices has been solved 70’s by Robinson. In many applications one needs construct connected control their edges, but adaptation Robinson’s enumeration take this into account led formulas based on inclusion-exclusion principle, inducing high computational cost for uniform random sampling formula. present paper we propose two contributions. First enumerate new class DAGs, enriched with independent ordering children each vertex, according numbers edges. We obtain constructive recursive formula them (i.e. without using principle) decomposition scheme. Then show applicability our method proposing labelled same decomposition. As consequence able derive efficient samplers both models.