# Rainbow Mean Colorings of Graphs

## Document Type

Article

## Publication Date

1-1-2019

## Publication Title

Discrete Mathematics Letters

## Issue

2

## First page number:

18

## Last page number:

25

## Abstract

A mean coloring of a connected graph G of order 3 or more is an edge coloring c of G with positive integers where the average of the colors of the edges incident with each vertex v of G is an integer. This average is the chromatic mean of v. 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 chromatic mean index of c and the rainbow chromatic mean index of the graph G is the minimum chromatic mean index among all rainbow mean colorings of G. It is shown that the rainbow chromatic mean index exists for every connected graph of order 3 or more. The rainbow chromatic mean index is determined for paths, cycles, complete graphs, and stars.

## Keywords

chromatic mean; rainbow mean colorings; rainbow chromatic mean index

## Disciplines

Arts and Humanities | Fine Arts

## Language

English

## Repository Citation

Chartrand, G.,
Hallas, J.,
Salehi, E.,
Zing, P.
(2019).
Rainbow Mean Colorings of Graphs.
*Discrete Mathematics Letters*(2),
18-25.