Complement of the zero divisor graph of a lattice
Keywords:
Zero divisor graph, complement of the graph, Beck's conjecture, N-prime ideal, B-prime ideal, semiprime ideal, diameter, radius, centre, girth.Abstract
In this paper, we determine when \((\Gamma_I (L))^c\), the complement of the zero-divisor graph \((\Gamma_I (L))\) with respect to a semiprime ideal I of a lattice L, is connected and also determine its diameter, radius, centre and girth. Further, a form of Beck's conjecture is proved for \((\Gamma_I (L))\) when \(\omega((\Gamma_I (L))c) < \infty\). 10.1017/S0004972713000300Published
2014-01-27
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