çgm tdZddlmZddlZddlmZddgZejd dZ ejdZ dS) z3Functions for computing dominating sets in a graph.)chainN)arbitrary_elementdominating_setis_dominating_setc\t|}|t|}||vrtjd|d|h}t||}||z |z }|rM|}t|||z }||||z}||z}|M|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 Nznode z is not in G)setrnx NetworkXErrorpopadd)G start_with all_nodesrdominated_nodesremaining_nodesvundominated_nbrss Z/var/www/html/ai-engine/env/lib/python3.11/site-packages/networkx/algorithms/dominating.pyrr sJAI&y11 ?z???@@@ \N!J-((O/1NBO  ,    ! !qt99~5 1++++  , cfd|D}ttjfd|D}tt|z |z dkS)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 ch|]}|v| Sr.0nr s r z$is_dominating_set..]s+++QAFFqFFFrc3(K|] }|V dSNrrs r z$is_dominating_set..^s'"9"9A1Q4"9"9"9"9"9"9rr)rr from_iterablelen)r nbunchtestsetnbrss` rrrEsn0,+++&+++G u""9"9"9"9"9"9"999 : :D s1vv$& ' '1 ,,rr) __doc__ itertoolsrnetworkxr networkx.utilsr__all__ _dispatchablerrrrrr+s99,,,,,, 0 16666r-----r