Role coloring of graphs from rooted products

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Description	Size	Format
Role coloring of graphs from rooted products	244 KB	Adobe Acrobat PDF	Read	Download
DOI Доступ к ресурсу на сайте издателя			10.17223/20710410/68/6

Title: Role coloring of graphs from rooted products
Title: Ролевая раскраска графов из корневых произведений
Creator: Komathi, M.
|
Ragukumar, P.
Date: 2025
DOI: 10.17223/20710410/68/6
Description: A k-role coloring is an assignment of k colors to the vertices of a graph such that if any two vertices receive the same color, then the set of colors assigned to their neighborhood will also be the same. Any graph with n vertices can have n-role coloring. Although it is easy to determine whether a graph with n vertices accepts a 1-role coloring, the challenge of k-role coloring is known to be difficult for k > 2. In fact, k-role coloring is known to be NP-complete for k > 2 on general graphs. In this paper, we determine k-role coloring of the rooted product of various graphs.