# k-TUPLE DOMATIC IN GRAPHS

Author

Department of Mathematics, University of Mohaghegh Ardabili

Abstract

For every positive integer k, a set S of vertices in a graph G = (V;E) is a k-
tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices
and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum
cardinality of a k-tuple dominating set of G is the k-tuple domination number of
G. When k = 1, a k-tuple domination number is the well-studied domination
number. We define the k-tuple domatic number of G as the largest number of
sets in a partition of V into k-tuple dominating sets. Recall that when k = 1,
a k-tuple domatic number is the well-studied domatic number. In this work, we
derive basic properties and bounds for the k-tuple domatic number.

Keywords

Article Title [Persian]

### دماتیک کاتایی در گرافها

Author [Persian]

• عادل کاظمی
دانشکده علوم ریاضی – دانشگاه محقق اردبیلی- اردبیل
Abstract [Persian]

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Keywords [Persian]

• مجموعه احاطه کننده K-تایی
• عدد احاطه کنندگی K-تایی
• عدد دماتیک K-تایی