Power graphs provide an innovative way to visualise and analyse the algebraic structure of finite groups. In a power graph, the elements of a finite group serve as vertices, and an edge is drawn ...

For any integer 𝑘 ≥ 2, a graph 𝐺 is called 𝑘-leaf-connected if |V(G)|≥k+1 and given any subset 𝑆 ⊆ 𝑉(𝐺) with |S|=k,G always has a spanning tree 𝑇 such that 𝑆 is precisely the set of leaves of ...

Commuting graphs have emerged as a powerful framework for elucidating complex relationships within finite group theory. In these graphs, vertices typically represent non-central elements of a group, ...