The orbit graph for some finite solvable groups (original) (raw)

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 ν_1 and ν_2 are adjacent in the graph whenever ν_1g= ν_2, where ν_1, ν_2∈ 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.