University of MazandaranCaspian Journal of Mathematical Sciences (CJMS)1735-06112220130501k-TUPLE DOMATIC IN GRAPHSدماتیک کاتایی در گرافها105112450ENA. P. KazemiDepartment of Mathematics, University of Mohaghegh ArdabiliJournal Article20120512For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- <br />tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices <br />and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum <br />cardinality of a k-tuple dominating set of G is the k-tuple domination number of <br />G. When k = 1, a k-tuple domination number is the well-studied domination <br />number. We define the k-tuple domatic number of G as the largest number of <br />sets in a partition of V into k-tuple dominating sets. Recall that when k = 1, <br />a k-tuple domatic number is the well-studied domatic number. In this work, we <br />derive basic properties and bounds for the k-tuple domatic number....http://cjms.journals.umz.ac.ir/article_450_376603f729effe72173d9d24b2684890.pdf