A Study on Eulerian Proper Power Graph for finite groups
Abstract
G be a finite group. The power graph ℒ (G) is an undirected graph with vertex set G where two distinct vertices u and v in ℒ (G) are adjacent if u = vα or v = uβ for some α, β in N. The proper power graph denoted by ℒ /(G) of the group G is the graph obtained by deleting the identity element from G. i.e, ℒ / (G) = ℒ / (G/e). In this paper, we Examine the Eulerian graph property for proper power graphs of certain finite groups such as S3 , D4, Q8, D5, A4, D6, Q12, D7.