Injective coloring of some graph operations

Injective chromatic number of lexicographic product of two graphs

“…In this section the injective chromatic number of lexicographic products are obtained. For any two arbitrary graphs G and H, the injective chromatic number of G[H] is bounded, it is established in [6].…”

“…Song and J. Yue. [6] obtained some sharp bounds (or exact values) of injective chromatic number of Cartesian product, direct product, lexicographic product, union, join, and disjunction of graphs.…”

On the Packing Partitioning Problem on Directed Graphs

“…For such a function f , the set of color classes {v ∈ V (G) | f (v) = i} 1≤i≤k is an injective k-coloring of G (or simply an injective coloring if k is clear from the context). The minimum k for which a graph G admits an injective k-coloring is the injective chromatic number χ i (G) of G. Injective colorings were introduced in [11], and further studied in [3,17,24,27] for just some examples.…”