A Note on Rainbow Mean Indexes of Paths
Gary Chartrand, James Hallas, Ebrahim Salehi, Ping Zhang · Discrete Mathematics Letters · 2021
For an edge coloring c of a connected graph G of order 3 or more with positive integers, the chromatic mean of a vertex v of G is defined as that vertex color which is the average of the colors of the edges incident with v.Only those edge colorings c for which the chromatic mean of every vertex is a positive integer are considered.If distinct vertices have distinct chromatic means, then c is called a rainbow mean coloring of G.The maximum vertex color in a rainbow mean coloring c of G is the rainbow mean index of c, while the rainbow mean index of G is the minimum rainbow mean index among all rainbow mean colorings of G.In this note, we prove that every path Pn of order n ≥ 3 has rainbow mean index n except P4 which has rainbow mean index 5.