Finite Simple Graphs and Their Associated Graph Lattices

Authors

James B. Hart, Middle Tennessee State UniversityFollow
Brian Frazier, University of MississippiFollow

Abstract

In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Hart, James B. and Frazier, Brian (2018) "Finite Simple Graphs and Their Associated Graph Lattices," Theory and Applications of Graphs: Vol. 5: Iss. 2, Article 6.
DOI: 10.20429/tag.2018.050206
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/6