# On the Rainbow Mean Indexes of Caterpillars

## Document Type

Article

## Publication Date

12-1-2023

## Abstract

Let G be a simple connected graph and c an edge coloring with colors that are positive integers. Given a vertex v of G, we define its chromatic mean, denoted by cm(v), as the average of the colors of the incident edges. If cm(v) is an integer for each v ∈ V (G) and distinct vertices have distinct chromatic means, then c is called a rainbow mean coloring. The maximum chromatic mean of a vertex in the coloring c is called the rainbow mean index of c and is denoted by rm(c). On the other hand, the rainbow mean index of G, denoted by rm(G), is the minimum value of rm(c) among all rainbow mean colorings c of G. In this paper, we determine the rainbow mean indexes of families of caterpillars, including brooms, and double brooms.

## Recommended Citation

Garciano, A. D., Marcelo, R. M., Ruiz, M. P., & Tolentino, M. A. C. (2023). On the Rainbow Mean Indexes of Caterpillars: Discrete and Computational Geometry, Graphs, and Games. Thai Journal of Mathematics, 21(4), 821–834. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1548