سال انتشار: ۱۳۸۶

محل انتشار: سی و هشتمین کنفرانس ریاضی ایران

تعداد صفحات: ۳

نویسنده(ها):

O FAVARON – Department of Mathematics, Univ Paris-Sub, LRI, UMR 8623, Orsay, F-91405, France.
H KARAMI – Faculty of Mathematics, Sharif University of Technology, Tehran, Iran
S.M SHAIKHOLESLAM – Department of Mathematics, Azarbayejan University of Tarbiat Moallem, Azarshahr, Tabriz, Iran

چکیده:

A paired-dominating set of a graph G=(V,E) with no isolated vertex is a dominating set of vertices inducing a graph with a perfect matching. The paired-domination number of G, denoted by ypr(G), is the minimum caredinality of a paired-dominating set of G. We consider graphs of order n≥۶, minimum degree δ such that G and G’ do not have isolated vertex and we shall prove that
– if ypr (G) > 4 and ypr(G’) > 4, then ypr(G) + ypr(G’) ≤ ۳+ min {δ(G), δ(G’)}.
– if δ(G) ≥ ۲ and δ(G’)≥ ۲, then ypr(G) + ypr(G’) ≤ ۲n/3 + 4 and ypr(G) + ypr(G’) ≤ ۲n/3 + 2 if moreover n ≥ ۲۱٫