Rainbow Dynamic Coloring in Few Brick Product Graphs
Gayathri Annasagaram · Communications on Applied Nonlinear Analysis · 2025
Consider a connected graph that is nontrivial, defined as a coloring c : V (G) → {1, 2, . . . ., k}, k ∈ N of the vertices of G. A rainbow dynamic coloring of a graph is a dynamic coloring, and a minimum number of colors required, such that every pair of vertices is connected by at least one path whose within vertices have different colors. The minimum k for which k-vertex coloring exists is called the rainbow dynamic coloring of G, denoted by rdyc(G). In this paper, we determine the rdyc of some graphs of brick products C(2n, m, r) associated with odd cycles for m = 1. Objectives: To find the rdyc of few brick product graphs. Conclusions: In this paper, we obtain the rainbow dynamic coloring of fewbrick product graphs C(2n, m, r) for m = 1 and r = 3, 5, 7.