The description of the correction
Authors have identified errors in the paper originally submitted and finally approved (after the acceptance) by the Authors.
On page 74, case 2 second line and third line highlighted part to be changed.
By Proposition 2.2, as includes an odd cycle. Assign the proper coloring to the vertices as , . Thus, a minimum of three colors are required for proper coloring. Therefore .
On page 74, an error in the symbol of statement of Theorem 3.3.
On page 75, third paragraph second line of case when = 6, 4 is to be written as 3.
In this case the set or are only -sets of graph . According to Lemma – 3.1, and by Lemma – 3.2, . Allocating several colors to the vertices of the -set that is equal to in order to determine its optimal coloring. Now we use number of colors to color the remaining vertices.
On page 75, Case 1 last line in place of 6, it should be 5.
The coloring pattern can be defined as Here every vertex dominates the vertices of at least one color class. As a result, the proper coloring creates a dominator coloring for the relevant graph. Therefore, .
On page 75, Case 2 title is mentioned incorrect.
Case 2: ,
On page 75, In the line just above the Fig. 1, in place of six colors there must be five colors.
A dominator coloring of using five colors is shown in Fig. 1.