7th Article " Partitioning the arcs of a digraph into a star forest of the underlying graph with prescribed orientation properties."

Nur Fatmawati
16611047

Partitioning the arcs of a digraph into a star forest of the underlying graph with prescribed orientation properties.

A star is a special kind of tree. As with any tree, stars may be encoded by a Prufer sequence the Prufer sequence for a star K₁consists of k − 1 copies of the center vertex. Several graph invariants are defined in terms of stars. Star arboricity is the minimum number of forests that a graph can be partitioned into such that each tree in each forest is a star, and the star chromatic number of a graph is the minimum number of colors needed to color its vertices in such a way that every two color classes together form a subgraph in which all connected components are stars. And a star forest is a collection of vertex disjoint stars.