حد أدنى وحد أعلى لعدد السيطرة من المرتبة 2 ﻠ من أجل و عدد كيفي.
Abstract
ليكن لدينا البيان من المرتبة مع مجموعة الرؤوس ومجموعة الأضلاع . ولتكن 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 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.Downloads
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