Homotopy type of the independence complexes of a family of regular bipartite graphs

TL;DR

This paper investigates the topological structure of independence complexes in a specific family of regular bipartite graphs, revealing they are homotopy equivalent to a wedge sum of spheres.

Contribution

It introduces a new family of regular bipartite graphs and determines their independence complexes' homotopy types as wedge sums of spheres.

Findings

Independence complexes are homotopy equivalent to wedge sums of spheres.

The homotopy type depends on the graph's regularity and bipartite structure.

Provides a topological characterization of a new graph family.

Abstract

In this article, we define a family of regular bipartite graphs and show that the homotopy type of the independence complexes of this family is the wedge sum of spheres of certain dimensions.