کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423334 | 1342323 | 2015 | 10 صفحه PDF | دانلود رایگان |
We consider two general frameworks for multiple domination, which are called ãr,sã-domination and parametric domination. They generalise and unify {k}-domination, k-domination, total k-domination and k-tuple domination. In this paper, known upper bounds for the classical domination are generalised for the ãr,sã-domination and parametric domination numbers. These generalisations are based on the probabilistic method and they imply new upper bounds for the {k}-domination and total k-domination numbers. Also, we study threshold functions, which impose additional restrictions on the minimum vertex degree, and present new upper bounds for the aforementioned numbers. Those bounds extend similar known results for k-tuple domination and total k-domination.
Journal: Discrete Mathematics - Volume 338, Issue 11, 6 November 2015, Pages 2095-2104