Graph Coloring with inversion in the non-Deranged Permutations

Abstract

In this paper, we investigate graph coloring with inversion in non-deranged permutations, the permutation which fixes the first element in the permutations.This was first accomplished by performing some calculations on this strategy using prime numbers. . As a result, We observed that the chromatic number of any   in  is equal to and any  in  is equal to one. Similarly, the chromatic index of any in  is equal to  and any  in  is equal to zero. Results for this investigation established that chromatic number and chromatic index are related.