Royal Colorings of Graphs
Gary Chartrand, James Hallas, Ping Zhang · Ars Combinatoria · 2023
For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v . If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal k coloring. The minimum positive integer k for which a graph has a strong royal k -coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.