4 problems

Let $G$ be a graph, let its associated cubical set be given, and let $|G|$ denote the geometric realization of that cubical set. Suppose that $G$ satisfies the cubical approximatio…

Let $G_1$ be a cycle graph of length $5$, and let $G_n$ be the graphs defined recursively in the source via the discrete suspension construction. Let $A_i(G_n)$ denote the $i$th di…

Let $G_1$ be a cycle graph of length $5$, and let $G_n$ be the graphs defined recursively in the source via the discrete suspension construction. For each $n$, let…

Let $G$ be a graph, let $A_k(G)$ denote its $k$th discrete homotopy group, and let $\hc_k(G)$ denote its $k$th discrete singular cubical homology group. Suppose $n\geq 2$ and…