📘 graph theory

1. **Given the graph $G$ with vertices $v_1$ to $v_8$ and specified edges:** - **Vertex set $V$:** The set of all vertices is

1. **Problem Statement:** We need to find a nontrivial connected graph $G$ which satisfies the following properties: (a) Every bridge of $G$ is adjacent to an edge that is not a br

1. **Problem 9(a):** Show that if $\delta(G) \geq \binom{n}{2}$ then the simple graph $G$ with $n$ vertices is connected. 2. **Step 1:** Recall $\delta(G)$ is the minimum degree am