MMN-3620

# Graph with respect to superfluous elements in a lattice

**Tapatee Sahoo**, Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India,`tapateesahoo96@gmail.com`

**Harikrishnan Panackal**, Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India,`pk.harikrishnan@manipal.edu`

**Kedukodi Babushri Srinivas**, Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India,`babushrisrinivas.k@manipal.edu`

**Syam Prasad Kuncham**, Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India,`syamprasad.k@manipal.edu`

## Abstract

We consider superfluous elements in a bounded lattice with 0 and 1, and introduce various types of graphs associated with these elements. The notions such as, superfluous element graph ($S(L)$), join intersection graph ($JI(L)$) in a lattice, and in a distributive lattice, superfluous intersection graph ($SI(L)$) are defined. Dual atoms play an important role to find connection between the lattice-theoretic properties and those of corresponding graph-theoretic properties. Consequently, we derive some important equivalent conditions of graphs involving the cardinality of dual atoms in a lattice. We provide necessary illustrations and investigate properties such as diameter, girth and cut vertex of these graphs.

Vol. 23 (2022), No. 2, pp. 929-945

DOI: 10.18514/MMN.2022.3620