The Rainbow Mean Index of Corona Product of Graphs

In a connected graph G with at least three vertices, an edge coloring c assigns positive integers to the edges. The chromatic mean of a vertex v is determined 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 every 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. In this study, we calculate the rainbow mean index of corona product of Px◦H; G◦Py and Px◦Py, where G and H are regular graphs. In addition, we calculate the rainbow mean index of the join graph G∨K1, where G is a regular graph.