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- Title
COMPLEMENT OF THE ZERO DIVISOR GRAPH OF A LATTICE.
- Authors
JOSHI, VINAYAK; KHISTE, ANAGHA
- Abstract
In this paper, we determine when $\mathop{({\Gamma }_{I} (L))}\nolimits ^{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 (\mathop{({\Gamma }_{I} (L))}\nolimits ^{c} )\lt \infty $.
- Subjects
DIVISOR theory; LATTICE theory; GRAPHIC methods; COMMUTATIVE rings; DIAMETER; RADIUS (Geometry)
- Publication
Bulletin of the Australian Mathematical Society, 2014, Vol 89, Issue 2, p177
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972713000300