In this article, we consider the bipartite graphs $K_2 \times K_n$. We first show that the connectedness of the neighborhood complex $\mathcal{N}(K_{n+1}^{K_n}) =0$. Further, we show that Hom$(K_2 \times K_{n}, K_{m})$ is homotopic to $S^{m-2}$, if $2\leq m .
@article{10_37236_5312,
author = {Nandini Nilakantan and Samir Shukla},
title = {Neighborhood complexes of some exponential graphs},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5312},
zbl = {1336.05045},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5312/}
}
TY - JOUR
AU - Nandini Nilakantan
AU - Samir Shukla
TI - Neighborhood complexes of some exponential graphs
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5312/
DO - 10.37236/5312
ID - 10_37236_5312
ER -
%0 Journal Article
%A Nandini Nilakantan
%A Samir Shukla
%T Neighborhood complexes of some exponential graphs
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5312/
%R 10.37236/5312
%F 10_37236_5312
Nandini Nilakantan; Samir Shukla. Neighborhood complexes of some exponential graphs. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5312
