REPRESENTATION OF A LATTICE BY A GRAPH WITH RESPECT TO AN IDEAL AND ITS CHARACTERIZATION
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In this paper a graph of a nite lattice L with respect to an ideal I is de ned and is denoted by GI (L). We demonstrate essential ndings that connect ideals and graph representations. Furthermore, we explore the construction of the incidence matrix P for GI (L) and utilize it as a context table to derive the corresponding Concept Lattice LP . In doing so, we uncover intriguing relationships between GI (L) and LP . The results obtained in this study o er valuable insights into the interactions between nite lattices, their graph representations, and the signi cance of prime ideals. The implications of these ndings can have applications in various domains, such as lattice theory and graph theory.
Abstract
In this paper a graph of a nite lattice L with respect to an ideal I is de ned and is denoted by GI (L). We demonstrate essential ndings that connect ideals and graph representations. Furthermore, we explore the construction of the incidence matrix P for GI (L) and utilize it as a context table to derive the corresponding Concept Lattice LP . In doing so, we uncover intriguing relationships between GI (L) and LP . The results obtained in this study o er valuable insights into the interactions between nite lattices, their graph representations, and the signi cance of prime ideals. The implications of these ndings can have applications in various domains, such as lattice theory and graph theory.
참고문헌 (6)
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- F. Harary, "Graph Theory" (2018), Narosa publishing house
- G. Birkoff, "Lattice theory", Amer.Math.Soc.Colloq. publ, 25 (1973)
- S. Bhavanari, "Graph of a nearring with respect to an ideal", Communications in Algebra, 38(5), pp.1957~1967 (2010)