Order divisor graphs of finite groups
  The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having different orders are adjacent provided that o(a) divides o(b) or o(b) divides o(a). 
Shafiq Ur Rehman, Abdul Qudair Baig, Muhammad Imran, and Zia Ullah   Khan
math.CO math.GR