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The article proposes the implicit exhaustive search procedure based on the triangle decomposition of graphs for determining the maximal clique in the arbitrary undirected graph G in polynomial time; it has allowed developing an exact algorithm for solving the problem with time complexity not exceeding ) ( 7 n O , where n is the number of vertices in the graph G.Index Terms-Мaximal independent set, click, vertex cover, decomposition of a graph into triangles 2 An Approach to Determination of Maximal Cliques in Undirected Graphs

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Ìåòîä ïåðå÷èñëåíèÿ ìàêñèìàëüíûõ íåçàâèñèìûõ ìíîaeåñòâ â íåîðèåíòèðîâàííûõ ãðàôàõ Íà îñíîâå ðàíãîâîãî ïîäõîäà ïðåäëîaeåí ìåòîä ïåðå÷èñëåíèÿ ìàêñèìàëüíûõ íåçàâèñèìûõ ìíîaeåñòâ íåîðèåíòèðîâàííîãî ñâÿçíîãî ãðàôà ñ âðåìåííîé ñëîaeíîñòüþ, â ñðåäíåì íå ïðåâûøàþùåé O (n 6), ãäå n-÷èñëî âåðøèí â ãðàôå, äëÿ ãðàôîâ, íå ñîäåðaeàùèõ ðàçäåëÿþùèõ âåðøèí, ðàçìåðíîñòü êîòîðûõ íå ïðåâûøàåò n = 125. Ê ë þ ÷ å â û å ñ ë î â à: ìàêñèìàëüíîå íåçàâèñèìîå ìíîaeåñòâî, êëèêà, âåðøèííîå ïîêðûòèå.

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