On Power Graph Representation of Γ_1-nonderanged Permutation Group
DOI:
https://doi.org/10.56919/usci.2541.006Keywords:
Group, permutation group, nonderanged permutation group, power graph, adjacency matrixAbstract
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.
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