All Questions

Consider the infinite 3-regular tree. Pick a vertex $C$, the "center". For any integer $L\ge 1$ consider the closed ball, in the graph distance, of radius $L$ around $C$. Let $T_L$ be the induced ...

The comb is the undirected simple graph with nodes $\mathbb{N} \times \mathbb{N}$ where $\mathbb{N} \ni 0$ and edges $$ \{\{(m,n), (m,n+1)\}, \{(m,0), (m+1,0)\} \;|\; m \in \mathbb{N}, n \in \mathbb{N}...

Let $G=(V,E)$ be a connected countably infinite $k$-regular simple graph (no loops or multiple edges). For $A$ a finite subset of $V$, let me denote by $G_A=(A,E_A)$ the induced subgraph with vertex ...