Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9514621 | Electronic Notes in Discrete Mathematics | 2005 | 10 Pages |
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(Zn) is connected, complete, bipartite, planar or has a cycle. Next we characterize finite graphs which are the intersection graphs of Zn and determine the set of all non-isomorphic graphs of Zn for a given number of vertices. We also determine the values of n for which the graph of Zn is Eulerian and Hamiltonian.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ivy Chakrabarty, Shamik Ghosh, T.K. Mukherjee, M.K. Sen,