Coloring the vertices of a graph [Formula: see text] according to certain conditions can be considered as a random experiment and a discrete random variable [Formula: see text] can be defined as the number of vertices having a particular color in the proper coloring of [Formula: see text]. The concepts of mean and variance, two important statistical measures, have also been introduced to the theory of graph coloring and determined the values of these parameters for a number of standard graphs. In this paper, we discuss the coloring parameters of the Mycielskian of certain standard graphs.

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Coloring the vertices of a graph [Formula: see text] according to certain conditions can be considered as a random experiment and a discrete random variable (r.v.) [Formula: see text] can be defined as the number of vertices having a particular color in the proper coloring of [Formula: see text] and a probability mass function for this random variable can be defined accordingly. In this paper, we extend the concepts of mean and variance to a modified injective graph coloring and determine the values of these parameters for a number of standard graphs.

Coloring the vertices of a graph [Formula: see text] according to certain conditions is a random experiment and a discrete random variable [Formula: see text] is defined as the number of vertices having a particular color in the given type of coloring of [Formula: see text] and a probability mass function for this random variable can be defined accordingly. An equitable coloring of a graph [Formula: see text] is a proper coloring [Formula: see text] of [Formula: see text] which an assignment of colors to the vertices of [Formula: see text] such that the numbers of vertices in any two color classes differ by at most one. In this paper, we extend the concepts of arithmetic mean and variance, the two major statistical parameters, to the theory of equitable graph coloring and hence determine the values of these parameters for a number of standard graphs.