Hamiltonicity of the Complete Double Vertex Graph of some Join Graphs

Abstract

The complete double vertex graph M2(G) of G is defined as the graph whose vertices are the 2-multisubsets of V (G), and two of such vertices are adjacent in M2(G) if their symmetric difference (as multisets) is a pair of adjacent vertices in G. In this paper we exhibit an infinite family of graphs G (containing Hamiltonian and non-Hamiltonian graphs) for which M2(G) are Hamiltonian.