Join maximal element graph of lattice modules

Document Type : Research Paper

Authors

1 Department of Mathematics‎,‎ Savitribai Phule Pune University, Pune‎, ‎India

2 Department of Mathematics‎,‎ Fergusson College(Autonomus), Pune‎, ‎India

3 Bharati Vidyapeeth Deemed to be University College of Engineering, Pune‎, ‎India

Abstract

Let $\pounds$ be a $C$-lattice and $M$ be a lattice module over $\pounds$‎. ‎The join maximal element graph $\mathbb{G}(M)$ is a simple‎, ‎undirected graph with all proper non-zero elements of $M$ as vertices‎, ‎and two distinct vertices‎, ‎$N$ and $K$‎, ‎are adjacent if and only if $N\vee K\in Max(M)$‎, ‎where $Max(M)$ is the collection of all maximal elements of $M$‎. ‎In this paper‎, ‎some properties of the graph $\mathbb{G}(M)$ like diameter‎, ‎girth and clique number are investigated‎. ‎Also‎, ‎the interplay between the algebraic properties of $M$ and the properties of those graphs is studied‎.

Keywords

Main Subjects

References

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