D:\sbornik\...\TPEL\TPEL.DVI Mathematical Problems of Computer Science 32, 27{34, 2009. T he Stable Set N umber for the Str ong P r oduct of Gener alized Cycles S e va k H . B a d a lya n a n d S t e p a n E . Ma r ko s ya n Yerevan State University sevak badalyan@yahoo.com Abstract The strong product of an odd cycle and a generalized cycle and the strong product of two generalized cycles are investigated. For both cases a method is given to construct a stable set of vertices in product graph to achieve the known upper bound ®(G£H) · ½(G)£®(H) in case some conditions hold. For the stable set number of strong product of generalized cycles a lower bound is found. Refer ences [1 ] C. E . S h a n n o n , \ Th e z e r o -e r r o r c a p a c it y o f a n o is y c h a n n e l" , Tr a n s . 1 9 5 6 S ym p . In fo r - m a t io n Th e o r y, In s t . R a d io E n g . IT-2 , 8 -1 9 . [2 ] L . L o va s z , \ On t h e S h a n n o n c a p a c it y o f a g r a p h " , IE E E Transactions on Information Theory IT-25, p p . 1 -7 , 1 9 7 9 . [3 ] O. Or e , Theory of graphs, A m e r . Ma t h . S o c . Co llo q. P u b l., V o l. 3 8 , A m e r . Ma t h . S o c ., P r o vid e n c e , R . I., 1 9 6 2 . [4 ] M. R o s e n fe ld , \ On a p r o b le m o f C. E . S h a n n o n in g r a p h t h e o r y" , P roc. Amer. M ath. Soc.,p p . 3 1 5 -3 1 9 , 1 9 6 7 . [5 ] R . S . H a le s , \ N u m e r ic a l in va r ia n t s a n d t h e s t r o n g p r o d u c t o f g r a p h s " , Combin. Theory (B ) 15, p p . 1 4 6 -1 5 5 , 1 9 7 3 . [6 ] A . G. Ma r ko s ya n , \ Th e in t e r n a l s t a b ilit y n u m b e r in a c a r t e s ia n p r o d u c t o f s im p le c y- c le s " , Izvestiya Akademii Nauk Armyanskoy SSR . Seriya M atematika 6:5, p p . 3 8 6 -3 9 2 , 1 9 7 1 . [7 ] A . S c h r ijve r , Combinatorial Optimization. B e r lin -H e id e lb e r g -N e w Y o r k, S p r in g e r - V e r la g , 2 0 0 3 . [8 ] C. B e r g e , Graphs and Hypergraphs, N o r t h -H o lla n d , A m s t e r d a m , 1 9 7 3 . 2 7 2 8 The Stable Set Number for the Strong Product of Generalized Cycles àôÅ»Õ ³ñï³¹ñÛ³ÉÇ ³ÝϳËáõÃÛ³Ý ÃÇíÁ ÁݹѳÝñ³óí³Í óÇÏÉ»ñÇ Ñ³Ù³ñ ê. ´³¹³ÉÛ³Ý, ê. سñÏáëÛ³Ý ²Ù÷á÷áõÙ êáõÛÝ ³ß˳ï³ÝùáõÙ áõëáõÙݳëÇñíáõÙ ¿ ·ñ³ýÝ»ñÇ áõÅ»Õ ³ñï³¹ñÛ³ÉÇ ³ÝϳËáõÃÛ³Ý ÃíÇ Ï³åÁ ³ñï³¹ñÇãÝ»ñÇ ³ÝϳËáõÃÛ³Ý Ãí»ñÇ Ñ»ï, »ñµ ³ñï³¹ñÇãÝ»ñÇó Ù»ÏÁ ϳ٠»ñÏáõëÝ ¿É ÁݹѳÝñ³óí³Í óÇÏÉ »Ý: ¶ïÝí³Í ¿ Ýßí³Í ³ÝϳËáõÃÛ³Ý ÃÇíÁ áñáß å³ÛÙ³ÝÝ»ñÇ ¹»åùáõÙ ¨ ïñí³Í ¿ Ù»ÃṠѳٳå³ï³ëË³Ý ³ÝÏ³Ë µ³½ÙáõÃÛáõÝÁ ϳéáõó»Éáõ ѳٳñ: ÀݹѳÝñ³óí³Í óÇÏÉ»ñÇ áõÅ»Õ ³ñï³¹ñÛ³ÉÇ ³ÝϳËáõÃÛ³Ý ÃíÇ Ñ³Ù³ñ ·ïÝí³Í ¿ ëïáñÇÝ ·Ý³Ñ³ï³Ï³Ý: