عدد السيطرة في الجداء الديكارتي لحلقتين موجهتين Cm × Cn حيث n كيفي و m=9,10

Authors

  • سهيل محفوض
  • مازن مصطفى

Abstract

ليكن البيان  D( V, A ) بيان موجه من المرتبة  n مع مجموعة الرؤوس V(D) ومجموعة الأقواس A(D) .

ولتكن  S مجموعة جزئية  من مجموعة رؤوس البيان  V(D), نسمي S مجموعة سيطرة للبيان الموجه D إذا كان من أجل كل  رأس v ÎD – S  يوجد رأسu   من رؤوس المجموعة S بحيث أن  ÎA(D) (u , v) .

يرمز لعدد السيطرة  بـ g (D) والذي هو عدد عناصر أصغر مجموعة سيطرة.

الحلقة الموجهة من المرتبة n هي بيان موجه له n رأس و n قوس حيث أن كل رأس يتصل مع الرأس الذي يليه و الرأس الأخير يتصل بالرأس الأول .

في هذا البحث سوف نحسب عدد السيطرة للجداء الديكارتي لحلقتين موجهتين Cm x Cn في حالة m=9
و m=10  وn عدد كيفي .

Let   D(V, A) be a digraph of order n. V(D) and A(D) refer to the vertex and arc sets, respectively.

A subset S of vertex set V(D) is a dominating set of  D  if for each vertex vÎ D – S there exists a vertex u ÎS such  that (u, v) is an arc of D.

The domination number of D, g(D), is the order of a smallest dominating set of D.

Directed  cycle  of order  n  is a directed  graph has  n  vertex  (u0 ,u1 ,…….., un-1 )

and  n  arc:

i  ≤  n-2 }  U { (n-1,0)  }.  (i,i+1): 0 ≤ = { A(Cn)

In this paper we calculate the domination number of the Cartesian  product of

two  directed cycles Cm and Cn for m = 9, 10 and arbitrary n.

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Published

2018-12-09

How to Cite

1.
محفوض س, مصطفى م. عدد السيطرة في الجداء الديكارتي لحلقتين موجهتين Cm × Cn حيث n كيفي و m=9,10. TUJ-BA [Internet]. 2018Dec.9 [cited 2024May2];34(1). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5236

Issue

Vol. 34 No. 1 (2012): العلوم الأساسية

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