The orbit graph for some finite solvable groups - Omer, S. M. S. (2014)
Let G be a finite non-abelian solvable group and let Ω be the set of all subsets of commuting elements of size two in G. In this paper, we define a graph which is called an orbit graph whose vertices are non-central elements in Ω, where two vertices ν1 and ν2 are adjacent in the graph whenever ν1g = ν2, where ν1, ν2 ∈Ω, g ∈G. In this work, we find the orbit graph for some finite solvable groups where a group acts regularly and by conjugation on a set. Besides, some graph properties are found.