TY - JOUR

T1 - GRAPH WITH RESPECT TO SUPERFLUOUS ELEMENTS IN A LATTICE

AU - Sahoo, Tapatee

AU - Panackal, Harikrishnan

AU - Srinivas, Kedukodi Babushri

AU - Kuncham, Syam Prasad

N1 - Funding Information:
The authors express their deep gratitude to the referee(s)/editor(s) for their meticulous reading of the manuscript, and valuable suggestions that have definitely improved the paper. All the authors acknowledge the Manipal Institute of Technology (MIT), Manipal Academy of Higher Education, Manipal, India for their kind encouragement.
Publisher Copyright:
© 2022 Miskolc University Press

PY - 2022

Y1 - 2022

N2 - 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 connections 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.

AB - 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 connections 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.

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U2 - 10.18514/MMN.2022.3620

DO - 10.18514/MMN.2022.3620

M3 - Article

AN - SCOPUS:85135229193

VL - 23

SP - 929

EP - 945

JO - Miskolc Mathematical Notes

JF - Miskolc Mathematical Notes

SN - 1787-2405

IS - 2

ER -