Neighborhood Complexes of Some Exponential Graphs

Nandini Nilakantan, Samir Shukla

Abstract


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 $2\leq m <n$.


Keywords


Hom Complexes, Exponential Graphs, Discrete Morse Theory

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