Conditional coloring of some parameterized graphs

For integers k > 0 and r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r, d(v)} different colors. The smallest integer k for which a graph G has a conditional (k, r)-coloring is called the rth order conditional chromatic number, denoted by χr(G). For different values of r we obtain χr(G) of certain parameterized graphs viz., Windmill graph, line graph of Windmill graph, middle graph of Friendship graph, middle graph of a cycle, line graph of Friendship graph, middle graph of complete k-partite graph and middle graph of a bipartite graph.