The Rainbow Mean Coloring of Some Operations of Graphs

Maheswari, K.; Rajasekaran, G.

doi:10.28924/2291-8639-23-2025-304

Research Article

The Rainbow Mean Coloring of Some Operations of Graphs

K. Maheswari
G. Rajasekaran*

* Corresponding author

Abstract

In a connected graph G with a minimum of three vertices, an edge coloring c allocates positive numbers to the edges. The chromatic mean of a vertex v is calculated by averaging the colors of all incident edges, provided that the result remains a positive integer. A coloring c is a rainbow mean coloring if each vertex in G has a unique chromatic mean. The rainbow mean index of c is the highest chromatic mean assigned to any vertex, while the rainbow mean index of G is the smallest possible maximum chromatic mean for all valid rainbow mean colorings. This study calculates the rainbow mean index of tensor product graphs, specifically G₁ × G₂, where G₁ ∈ {C_q, K_q} and G₂ ∈ {C_t, K_t}; P_q × H, where H ∈ {C_t, K_t, W_t, F_t} and χ_rm(H) = t. We also compute the rainbow mean index for the rooted product of two graphs, the join of two graphs, and the caterpillar graph.

How to Cite

K. Maheswari, G. Rajasekaran, The Rainbow Mean Coloring of Some Operations of Graphs, Int. J. Anal. Appl. 23 (2025), 304. https://doi.org/10.28924/2291-8639-23-2025-304

BibTeX

@article{Maheswari2025,
  author  = {Maheswari, K. and Rajasekaran, G.},
  title   = {The Rainbow Mean Coloring of Some Operations of Graphs},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {304},
  doi     = {10.28924/2291-8639-23-2025-304}
}

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