Permutation graphs with co-inversion on Γ1 - non-deranged permutations

Abstract

In this paper, we define permutation graphs on Γ1 -non-deranged permutations using the set of co-inversion as edge set, and the values of permutation as the set of vertices. From the graphs, we observed that diameter and radius of the graph of any ω1  is one, the graph of any ωp-1 ∈ GΓ1p simple, the graph of ω1  is completed and other properties of the graphs were also observed.