Unit Graph of the Ring $$\boldsymbol{\mathbb{Z}_{m}\times\mathbb{Z}_{n}}$$

Graphs Defined on Rings: A Review

“…For better understanding of the structure of the graph based on the structure of the ring, the unit graphs of certain specific rings whose structures are well known were investigated in detail. In [262], the unit graph of the ring Z r × Z s , for any r, s ∈ N, was discussed exclusively, where the basic structural and traversal properties of the graph G + (Z r × Z s ) and its graph invariants were determined. Similarly, in [263], the rings of polynomials and power series over a ring were examined, and all standard properties and invariants of the unit graph of these rings were obtained, along with some results on the planarity of the graph.…”