On the Vanishing of Discrete Singular Cubical Homology for Graphs
On the Vanishing of Discrete Singular Cubical Homology for Graphs
We prove that if $G$ is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of $G$ is trivial in dimension $d$ for all $d\ge 2$. We also construct a sequence $\{G_d\}$ of graphs such that this homology is nontrivial in dimension $d$ for $d\ge 1$. Finally, we …