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Semi-complement graph of lattice modules

  • Narayan Phadatare
  • Vilas Kharat
  • Sachin Ballal
Foundations

Abstract

Let L be a C-lattice and M be a lattice module over L. In this paper, we introduce the semi-complement graph of M denoted by \(\Gamma (M)\) that is the undirected graph with all semi-complement elements of M as a vertex set, and two vertices X and Y are adjacent if and only if \(X\vee Y\) is a semi-complement element. In this paper, we investigate some properties of \(\Gamma (M)\) under some condition on M. For instance, we characterize non-connected graph \(\Gamma (M)\) of a principally generated comultiplication lattice module M over a C-lattice L.

Keywords

Minimal element Second element Semi-complement element 

Notes

Acknowledgements

We would like to thank Dr. Rupesh Shewale and Mr N.M. Shaikh for their suggestions for preparation of the present paper. The authors are very much thankful to the referee for valuable guidance.

Compliance with ethical standards:

Conflict of interest

The authors declare that there is no conflict of interests regarding the publishing of this paper.

Ethical approval:

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSavitribai Phule Pune UniversityPuneIndia

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