Some improper injective coloring parameters of graphs

Any vertex coloring protocol of a graph can be viewed as a random experiment of assigning colors to the vertices, whose random variable is defined as the number of vertices assigned a specific color in that coloring. Based on this idea, the statistical parameters of mean and variance have been extended to chromatic mean and chromatic variance for various proper vertex colorings of graphs in the literature. In this paper, the ideas of chromatic mean and chromatic variance of graphs concerning their improper injective coloring are introduced and determined for certain standard graphs.