# Necessary Conditions for Optimal Permissible Placement by the Height of the Transitive Directed Tree with One Root

## Keywords:

transitive directed graph, optimal placement## Abstract

In the graph theory the problem of the minimum placement of graph by the height, which is similarly formulated in [2] (the problem of minimum cut arrangement of graph), is known. The problem is NP-complete [3]. In the present paper a partial case of this problem, i.e. the problem of optimal permissible placement by the height of the transitive directed tree with one root (which is a such transitive directed graph, the arc base of which forms a directed tree with one root), is formulated. In this paper some new concepts are introduced and necessary conditions for optimal solving of the new formulated problem are given.

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*Mathematical Problems of Computer Science*,

*36*, 104–114. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/272

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