 Abstract: Let G = (V, E) be a finite, connected, undirected with no loops, multiple edges graph. Then the power dominator coloring of G is a proper coloring of G, such that each vertex of G power dominates every vertex of some color class. The minimum number of color classes in a power dominator coloring of the graph, is the power dominator chromatic number . Here we study the power dominator chromatic number for some special graphs such as Bull Graph, Star Graph, Wheel Graph, Helm graph with the help of induction method and Fan Graph. Suitable examples are provided to exemplify the results.

In this paper, Graph theoretical concepts are applied to analyze the reasons behind Arithmophobia commonly found among the students.Bull graph is used to epitomize Mild Arithmophobia which occurs when the preparation of students to face any test is deficient.Flower graph is used to represent Intense Arithmophobia. Wheel graph is used to depict the factors which desensitize Arithmophobia. Inferring information from these types of graphs is much more easier than inferring from a self map. This analysis will help in treating Arithmophobia and improve the student’s performance in Mathematics progressively. The benefits of using interactive graphical interface, graphs and graph theory metrics for a client centered analysis is also discussed