GRAPH WITH RESPECT TO SUPERFLUOUS ELEMENTS IN A LATTICE
Document Type
Article
Publication Title
Miskolc Mathematical Notes
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 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.
First Page
929
Last Page
945
DOI
10.18514/MMN.2022.3620
Publication Date
1-1-2022
Recommended Citation
Sahoo, Tapatee; Panackal, Harikrishnan; Srinivas, Kedukodi Babushri; and Kuncham, Syam Prasad, "GRAPH WITH RESPECT TO SUPERFLUOUS ELEMENTS IN A LATTICE" (2022). Open Access archive. 4895.
https://impressions.manipal.edu/open-access-archive/4895