Title

Constructing Copoint Graphs of Convex Geometries

Faculty Sponsor

Jon Beagley

College

Arts and Sciences

ORCID Identifier(s)

0000-0002-2990-5802, 0000-0002-5752-8012, 0000-0002-1064-9415

Document Type

Poster Presentation

Symposium Date

Summer 7-30-2018

Abstract

We work with copoint graphs of convex geometries. Copoint graphs can be used to study the complex and fairly recent field of convex geometries. Comparing copoints graphs and their convex geometries helps identify properties. We demonstrate that multiple convex geometries have the same underlying copoint graph. All graphs on one to five vertices can be represented as possible copoint graphs of some convex geometry. Furthermore, we construct several infinite classes of copoint graphs including the complete k-partite graph, path graph, centipede graph, ladder graph, comb graph, pom pom graph, shark teeth graph, and broken wheel graph.

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