Neighborhood complexes of some exponential graphs
Summary: 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 \(\mathrm{Hom}(K_2 \times K_{n}, K_{m})\) is homotopic to \(S^{m-2}\), if \(2\leqslant m <n\).
scientific article; zbMATH DE number 6583063
scientific article