CARTESIAN / TENSOR PRODUCT OF SOME NEW CLASS OF STAR – IN – COLORING GRAPHS

A proper coloring of a graph = ( , ) is a mapping : → {1,2,3, …}such that if = , then ( ) ≠ ( ). A graph G is said to admit star – in – coloring if it satisfies the following conditions. • No path of length three( ) is bicolored. • If any path of length two ( ) with end vertices are of the same color, then the edges of are directed towards the middle vertex. In this paper, we have proved that the splitting graph of fan graph, the splitting graph of double fan graph, Cartesian product of path and fan graph, Cartesian product of path and double fan graph, tensor product of path and fan graph, tensor product of path and double fan graph and Cartesian product of and the path graph is star – in – coloring graphs. In addition, we have given the general pattern of colors for all these graphs and their star – in – chromatic number.