An injective coloring of a given graph G = (V; E) is a vertex coloring of G such that any two vertices with common neighbor receive distinct colors. An e-injective coloring of a graph G is a vertex coloring of G such that any two vertices with common edge neighbor receive distinct colors; in other words, if u and v are the end of a path P4 of graph G, then they are assigned with different labels. With this new definition, we want to take a review at injective coloring of a graph from the new point of view. We also investigate the e-injective coloring of some standard graphs.
