Forbidden subgraphs of TI-power graphs of finite groups

Abstract

Given a finite group GG with identity ee, the TI-power graph (trivial intersection power graph) defined on GG, denoted by Γ(G)\Gamma \left(G), is an undirected graph with vertex set GG where distinct vertices aa and bb are adjacent if ⟨a⟩∩⟨b⟩={e}\langle a\rangle \cap \langle b\rangle =\left\{e\right\}. We classify all finite groups whose TI-power graph is claw-free, K1,4{K}_{1,4}-free, C4{C}_{4}-free, and P4{P}_{4}-free. In addition, we classify the finite groups whose TI-power graph is a threshold graph, a cograph, a chordal graph, and a split graph.

Keywords

• ti-power graphs
• forbidden subgraphs
• finite groups
• 05c25