Abstract   In this paper we consider the intersection graph G(R) of nontrivial left ideals of a ring R. We characterize the rings  R  for which the graph  G ( R ) is disconnected and obtain several necessary and sufficient conditions on a ring  R  such that  G ( R ) is complete. For a commutative ring  R  with identity we show that  G ( R ) is complete if and only if   G  (  R  [  x  ]  )   is also so. In particular, we determine the values of  n  for which   G  (   Z  n   )   is connected, complete, bipartite, planar or has a cycle. Next we characterize finite graphs which are the intersection graphs of    Z  n    and determine the set of all non-isomorphic graphs of    Z  n    for a given number of vertices. We also determine the values of n for which the graph of    Z  n    is Eulerian and Hamiltonian.
['Ivy Chakrabarty', 'Shamik Ghosh', 'Tilottama Mukherjee', 'M. K. Sen']
Intersection graphs of ideals of rings