Improper Injective Coloring Parameters of Certain Cycle-Related Graphs

Abstract

Any vertex coloring of a graph can be viewed as a random experiment of assigning colors to the vertices, whose random variable is defined based on the number of vertices assigned a particular color in that coloring. Based on this, the statistical parameters of mean and variance have been extended to chromatic mean and chromatic variance for various vertex colorings of graphs in the literature. In this article, the ideas of chromatic mean and chromatic variance of cycle-related graphs with respect to their improper injective coloring are investigated.

Keywords: Improper coloring; injective coloring; chromatic sum; chromatic mean; chromatic variance.

2010 Mathematics Subject Classification. 05C15, 05C38, 62A01