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