Abstract

For a group G with generating set S = {s₁,s₂,…,s_k}, the G-graph of G, denoted Γ(G,S), is the graph whose vertices are distinct cosets of ⟨s_i⟩ in G. Two distinct vertices are joined by an edge when the set intersection of the cosets is nonempty. In this paper, we study the existence of Hamiltonian and Eulerian paths and circuits in Γ(G,S).

Keywords

Groups, graphs, generators

Mathematical Subject Classification

Primary: 05C25, 20F05

Authors