2023/10/06 by Manisha, Parveen, Kumar, Jitender
#05C25 #20D15 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2310.04161
The power graph P(G) is the simple undirected graph with group elements as a vertex set and two elements are adjacent if one of them is a power of the other. The order supergraph S(G) of the power graph P(G) is the simple undirected graph with vertex set G in which two vertices x and y are adjacent if o(x)\vert o(y) or o(y)\vert o(x). In this paper, we classify all the finite groups G such that the order supergraph S(G) is the line graph of some graph. Moreover, we characterize finite groups whose order supergraphs are the complement of line graphs.