A note on co-maximal graphs of commutative rings

Abstract

Let be a commutative ring with unity. The co-maximal graph is the graph with vertex set and two vertices and are adjacent if . In this paper, we characterize rings for which the co-maximal graph is a line graph of some graph and determine rings for which is Eulerian or Hamiltonian. We also find the diameter and girth of .

Keywords

• finite commutative ring
• maximal ideal
• co-maximal graph
• line graph