• FRACTIONAL OUT-DOMINATION NUMBER OF AN OUT-TREE

K. Muthu Pandian*

Abstract


An out-dominating function (ODF) of a digraph  is a function  such that  for all , where  consists of  with all vertices adjacent from it. For a real valued function, the weight of  is . The fractional out-domination number of a digraph , denoted , equals the minimum weight  of an ODF of . In this paper, we develop a method for finding  for an out-tree that satisfies specific condition. A supporting proof for this method is also given. We also apply this method to the out-trees directed path and directed star.


Keywords


Digraphs, Out-dominating function, Minimal out-dominating function, fractional out-domination number , out-tree, directed path, directed star.

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