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Bounds on perfect k-domination in trees: an algorithmic approach

Chaluvaraju B., Vidya K. A.

Opuscula Mathematica

2012

Vol. 32, no. 4

707-714

Let k be a positive integer and G = (V, E) be a graph. A vertex subset D of a graph G is called a perfect k-dominating set of G if every vertex v of G not in D is adjacent to exactly k vertices of D. The minimum cardinality of a perfect k -dominating set of G is the perfect k-domination number γkp (G ). In this paper, a sharp bound for γkp (T) is obtained where T is a tree.