Hamiltonicity of the Complete Double Vertex Graph of some Join Graphs

Abstract

The complete double vertex graph $M_2(G)$ of $G$ is defined as the graph whose vertices are the $2$-multisubsets of $V(G)$, and two of such vertices are adjacent in $M_2(G)$ 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 $M_2(G)$ are Hamiltonian.

8 pages, 1 figure. The results presented in this article were presented in preprint arXiv:2007.00115 which was splitted into two papers