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COMPLEMENT OF THE ZERO DIVISOR GRAPH OF A LATTICE

Part of: Graph theory

Published online by Cambridge University Press:  11 June 2013

VINAYAK JOSHI  and
ANAGHA KHISTE
VINAYAK JOSHI*
Affiliation:
Department of Mathematics, University of Pune, Pune-411007, India email avanikhiste@gmail.com
ANAGHA KHISTE
Affiliation:
Department of Mathematics, University of Pune, Pune-411007, India email avanikhiste@gmail.com
*
✉vvj@math.unipune.ac.in
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Abstract

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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 $.

Keywords

zero divisor graphcomplement of the graphBeck’s conjectureN-prime idealB-prime idealsemiprime idealdiameterradiuscentregirth

MSC classification

Secondary: 05C15: Coloring of graphs and hypergraphs 05C40: Connectivity
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 177 - 190
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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