Unique Minimal Proper Roman Coloring of a Graph

Abstract

Suresh Kumar [12] introduced the notion of Roman Coloring of a graph, G which is an assignment of three colors {0, 1, 2} to the vertices of G such that a vertex with color, 0 must be adjacent to a vertex with color, 2 motivated from the Roman military defense strategy. The Proper coloring version of the Roman Coloring of a graph was introduced and studied by Suresh Kumar and Preethi K Pillai [13]. In this paper, we investigate the graphs having a unique minimal Proper Roman Coloring.