There is an undirected graph modeling highways in Texas, the vertices are cities and the edges are highways.
How would you model the property. "Even if you shut down one highway, you can get from any city in Texas to any other city in Texas" in graph-theoretic terms?
I know the graph must be connected by what other properties must be true of this graph?
On
A tree is a graph where there is exactly one unique path between any two vertices. So if there are at least two paths between two specific vertices, we have a cycle within the graph. Given that for each $a, b \in V(G)$, we have at least two paths from $a$ to $b$, the minimal case of this is if $G = C_{n}$, a cycle graph. Thus, 2-edge connectivity is the minimal case. That is, the minimal degree of any vertex is $2$.
It must be $2{}{}{}{}{}$-edge-connected.