ިsgm zdZddlmZddlZddlmZddgZejd dZ ejdZ y) z3Functions for computing dominating sets in a graph.)chainN)arbitrary_elementdominating_setis_dominating_setc$t|}| t|}||vrtjd|d|h}t||}||z |z }|r?|j }t|||z }|j |||z}||z}|r?|S)a\Finds a dominating set for the graph G. A *dominating set* for a graph with node set *V* is a subset *D* of *V* such that every node not in *D* is adjacent to at least one member of *D* [1]_. Parameters ---------- G : NetworkX graph start_with : node (default=None) Node to use as a starting point for the algorithm. Returns ------- D : set A dominating set for G. Notes ----- This function is an implementation of algorithm 7 in [2]_ which finds some dominating set, not necessarily the smallest one. See also -------- is_dominating_set References ---------- .. [1] https://en.wikipedia.org/wiki/Dominating_set .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms. http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf znode z is not in G)setrnx NetworkXErrorpopadd)G start_with all_nodesrdominated_nodesremaining_nodesvundominated_nbrss Q/var/www/html/venv/lib/python3.12/site-packages/networkx/algorithms/dominating.pyrr sJAI&y1 zl,?@@ \N!J-(O/1NBO     !qt9~5 1++++  c|Dchc] }|vs| }}ttjfd|D}tt|z |z dk(Scc}w)aChecks if `nbunch` is a dominating set for `G`. A *dominating set* for a graph with node set *V* is a subset *D* of *V* such that every node not in *D* is adjacent to at least one member of *D* [1]_. Parameters ---------- G : NetworkX graph nbunch : iterable An iterable of nodes in the graph `G`. See also -------- dominating_set References ---------- .. [1] https://en.wikipedia.org/wiki/Dominating_set c3(K|] }| ywN).0nr s r z$is_dominating_set..^s"9A1Q4"9sr)rr from_iterablelen)r nbunchrtestsetnbrss` rrrEs\0!+QAFq+G+ u"""9"99 :D s1v$& '1 ,,,s AAr) __doc__ itertoolsrnetworkxr networkx.utilsr__all__ _dispatchablerrrrrr(sQ9, 0 166r--r