A note on rainbow mean indexes of paths | [Discrete Mathematics Letters • 2022]

Author(s):

1. Gary Chartrand: Department of Mathematics, Western Michigan University,Kalamazoo, Michigan ,USA

2. James Hallas: Department of Mathematics, Western Michigan University,Kalamazoo, Michigan ,USA

3. Ebrahim Salehi: Department of Mathematical Sciences, University of Nevada Las Vegas,Las Vegas, Nevada 89154-4020,USA

4. Ping Zhang: Department of Mathematics, Western Michigan University,Kalamazoo, Michigan 49008-5248,USA

Abstract:

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.

Page(s): 57-59

DOI: 10.47443/dml.2021.0099

Published: Journal: Discrete Mathematics Letters, Volume: 8, Issue: 0, Year: 2022

Keywords:

Path , rainbow mean colorings , chromatic mean , rainbow mean index

References:

References are not available for this document.

Citations

Citations are not available for this document.

Citations

Downloads

Views