Publication Type:

Journal Article

Authors:

K. Abhishek

Source:

Discrete Mathematics, Algorithms and Applications, World Scientific Publishing Co. Pte Ltd, Volume 11, Issue 1 (2018)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058328421&doi=10.1142%2fS1793830919500071&partnerID=40&md5=d64f8c885a2d0bce3271a372e35a7454

Keywords:

graphs, Set-coloring, Strong set-coloring

Abstract:

In [S. M. Hegde, Set colorings of graphs, European J. Combin. 30 (2009) 986-995.] Hegde introduced the notion of set colorings of a graph G as an assignment of distinct subsets of a finite set X of n colors to the vertices of G such that all the colors of the edges which are obtained as the symmetric differences of the subsets assigned to their end-vertices are distinct. Additionally, if all the sets on the vertices and edges of G are the set of all nonempty subsets of X, then the coloring is said to be a strong set-coloring and G is said to be strongly set-colorable. In this paper, we report some new necessary conditions and propose a conjuncture for the sufficient condition for a graph to admit strong set-coloring. We also identify and characterize some new classes of graphs admitting strong set-coloring. In addition to these, we also propose strategies to construct infinite families graphs admitting strong set-coloring. © 2019 World Scientific Publishing Company.

Notes:

cited By 0; Article in Press

Cite this Research Publication

K. Abhishek, “Strongly set-colorable graphs”, Discrete Mathematics, Algorithms and Applications, vol. 11, no. 1, 2018.