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 R a + R b = 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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机译：令R为具有1的交换环。共同最大图Γ（R）是顶点集为R的图，如果R a + R b = R，则两个顶点a和b相邻。在本文中，我们描述了最大协图Γ（R）是某些图G的线图的环，并确定Γ（R）是欧拉或哈密顿量的环。我们还找到Γ（R）的直径和周长。
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