Non-intersection power graphs and co-prime graphs of finite groups

Abstract

In this paper, we define the non-intersection power graph of a finite group G as a graph whose vertex set is G, and edge set consists of unordered pairs {u, v} of vertices such that ⟨u⟩ ∩ ⟨v⟩ = {e}. We find some structural properties, planarity and independence number of non-intersection power graphs of finite groups. We classify all groups whose non-intersection power graph and co-prime graph are identical. Also we calculate some topological indices such as Wiener index, Harary index and Zagreb index of co-prime graphs of some groups.