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Register a new userLower and upper bounds of 2- domination number for m=6,7 and arbitrary n
حد أدنى و حد أعلى لعدد السيطرة من المرتبة 2 من أجل m=6,7 و عدد كيفي
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Tishreen University ورقة بحثية
Publication date
2017
fields
Mathematics
and research's language is
العربية
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Shamra Editor
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ليكن لدينا البيان من المرتبة مع مجموعة الرؤوس و مجموعة الأضلاع . و لتكن مجموعة جزئية من مجموعة رؤوس البيان , تدعى بأنها 2 - مجموعة سيطرة للبيان إذا كان لأجل كل رأس يوجد مجاورين له على الأقل من رؤوس المجموعة . كما و يرمز لعدد السيطرة من المرتبة 2 بالرمز و هو عدد عناصر أصغر 2- مجموعة سيطرة. في هذا البحث سوف سيتم إيجاد حد أدنى وحد أعلى لعدد السيطرة من المرتبة الثانية للجداء الديكارتي لمسارين في حالة m=6,7 و عدد كيفي.
Let be a graph of order n. with vertices and edges . A set D of vertices of a graph is called 2- dominating if every vertex has at least two neighbors in D. let denotes The 2- domination number of a graph G, , is the order of a smallest 2- dominating set of G. In this paper, we found lower and upper bounds of 2- domination number of the cartesian product of two paths for m=6,7 and arbitrary n.
References used
COCKAYNE,E. J; GAMBLE,B; SHEPHERD,B. An upper bound for the kdomination Number of a graph. J. Graph Theory 9(1985), 533-534
HANSBERG, A; VOLKMANN, L. Upper bounds on the k-domination number and the k-Roman domination number. Discrete Appl. Math. 157 (2009), 1634-1639
BLIDIAA,M; CHELLALIA,M; VOLKMANNB,L. Some bounds on the pdomination number in trees. Discrete Mathematics, 306 (2006), 2031 – 2037
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