10.11575/CDM.V16I3.71284
Shukla, Samir
Goyal, Shuchita
Singh, Anurag
Homotopy Type of Independence Complexes of Certain Families of Graphs
Contributions to Discrete Mathematics
2021
2020-10-08
2021-02-02
2022-01-21
2021-12-31
en
Article
110-5303-71284
10.11575/cdm.v16i3
10.11575/cdm.v16i3.71284.g55559
74-92 Pages
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
We show that the independence complexes of generalised Mycielskian of complete graphs are homotopy equivalent to a wedge sum of spheres, and determine the number of copies and the dimensions of these spheres. We also prove that the independence complexes of categorical product of complete graphs are wedge sum of circles, upto homotopy. Further, we show that if we perturb a graph $G$ in a certain way, then the independence complex of this new graph is homotopy equivalent to the suspension of the independence complex of $G$.
Contributions to Discrete Mathematics, Vol. 16 No. 3 (2021)