The relation graphs of finite lattices

Pramada Ramachandran; Teena Liza John

doi:10.26637/MJM0804/0147

Abstract

The relation graph of a finite lattice \(L\) is defined to be a simple graph with the elements of \(L\) as vertices and two distinct vertices are adjacent if and only if they are comparable in \(L\). We investigate the properties of relation graphs and characterize those lattices whose relation graphs are complete. The association between the relation graphs of isomorphic lattices is studied.

Keywords:

Lattice, simple graph, triangle free graph, isomorphism of lattices

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Pramada Ramachandran Department of Mathematics, St.Paul’s College, Kalamassery, Kochi-683503, Kerala, India.
Teena Liza John Department of Mathematics, TKM College of Engineering, Kollam-691005, Kerala, India.

Pages: 2194-2196
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

J. Abawajy, A. Kelarev, M. Chowdhury, Power Graphs: A Survey, Electronic Journal of Graph Theory and Applications, (2013), 125147,1 (2).

F. Harary, Graph Theory, Narosa Publishing House (1998).

H. M. Mulder, The Interval Function of a Graph, Mathematical Centre Tracts, Mathematisch Centrum, Amsterdam (1980).

P. Panigrahi, Bounds on spectral radius of power graphs of some finite groups, Invited Talk, CUSAT, ICRTGC 2018.

J. P. Tremblay, R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw Hill Edition, (1997)

B. Sebastian, A. Unnikrishnan, Kannan Balakrishnan, P. B. Ramkumar, Mathematical Morphology on Hypergraphs using vertex-hyperedge correspondence, ISRN Discrete Mathematics, (2014), 1-10.