Certain properties of the unit graph over the ring Z_p^k

Abstract

The unit graph G(R) is the graph in which two distinct vertices (distinct elements of R) are connected if the sum of the elements is a unit in R. In this paper, we study the unit graph G(Z_p^k), where k≥1 and p is a prime number. We provide some numerical invariants of G(Z_p^k), such as the clique number and the independence number. Furthermore, we investigate the eigensharp condition on the graph G(Z_p^k).