On Power Graph Representation of Γ_1-nonderanged Permutation Group

• DOI: 10.56919/usci.2541.006
• Publication Date: 2025-03-19T11:03:52Z
• Authors: Anas Yusuf; Almustapha Umar

Study’s Excerpt:

An undirected power graph representation of -nonderanged permutation group has been constructed. Ithas been proved that is connected for any and is neither regular nor complete except at The adjacency matrix of some selected graphs together with pictorial representations was also

Full Abstract: A -nonderanged permutation group is a permutation group such that where . In this paper, an undirected power graph representation of -nonderanged permutation group denoted by has been studied. It was proved, among other things, that the graph is connected for any and is neither regular nor complete except at Also, the maximum degree of is and the girth is three (3) for any while the diameter is one (1) for and two (2) for. Furthermore, the central vertex of the graph was proved to be for any and while the peripheral vertex is for p > 5. Lastly, the adjacency matrix of some selected graphs and their graphical representations were given to support our findings.