Star coloring for special graphs

Star coloring was carried out for the splitting graphs of Cycle, Path, Triangular snake graph, pie graph, Coconut tree graph, Friendship graph and Wheel graph. A proper coloring of a graph G can be termed as star-in-coloring, if the graph satisfied the following conditions: (1) no bicolored path for length three (2) the edges must be oriented towards the middle vertex when any path of length two has terminal vertices of the same color. The minimum number of color required to color a graph G as star-in-coloring can be termed as the star-in-chromatic number of the graph G (c_si (G))