Some results on set colorings of directed trees
Abstract
A set coloring of the digraph D is an assignment (function) of distinct subsets of a finite set X of colors to the vertices of the digraph, where the color of an arc, say (u, v) is obtained by applying the set difference from the set assigned to the vertex v to the set assigned to the vertex u which arc also distinct. A set coloring is called a strong set coloring if sets on the vertices and arcs are distinct and together form the set of all non empty subsets of X. A set coloring is called a proper set coloring if all the non empty subsets of X are obtained on the arcs of D. A digraph is called a strongly set colorable (properly set colorable) if it admits a strong set coloring (proper set coloring).
In this paper we find some classes of directed trees which admit a strong set coloring and construction of strongly set colorable directed tree Tn.
Copyright © 2020 Nisha Reena Nazareth, Lolita Priya Castelino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
N. R. Nazareth, L. P. Castelino, Some results on set colorings of directed trees, J. Math. Comput. Sci. 10 (2020), 403–411. https://doi.org/10.28919/jmcs/4425
BibTeX
@article{Nazareth2020,
author = {Nazareth, Nisha Reena and Castelino, Lolita Priya},
title = {Some results on set colorings of directed trees},
journal = {J. Math. Comput. Sci.},
volume = {10},
year = {2020},
pages = {403--411},
doi = {10.28919/jmcs/4425}
}