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
SN - 1787-2405
VL - 23
SP - 929
EP - 945
JO - Miskolc Mathematical Notes
JF - Miskolc Mathematical Notes
IS - 2
ER -