Rainbow Mean Index of Certain Derived Graphs

Mean coloring is an edge coloring c of a connected graph G of order 3 or more with positive integers if the chromatic mean of all vertices v of G are integers. The chromatic mean of a vertex v of G is given by cm(v)=∑ _e ∈ Eᵥ c(e)deg(v) where c(e) is the integers(colors) given to the edges incident to the vertex v. If each vertex has a distinct chromatic mean, then the edge coloring c is called a rainbow mean coloring. For a rainbow mean coloring c of a graph G, the maximum vertex color is the rainbow chromatic mean index, rm(c) of c. The rainbow mean index rm(G) of the graph G is defined as rm(G)=min (c): c is the rainbow mean coloring \ . In this paper, we determine the rainbow mean index of bistars and tadpole graphs. Also, we show that the rainbow mean index is same as the order for some derived graphs.