**Graph Theory Quiz**Given a cycle graph \( C_n \) and a complete graph \( K_n \) on \( n \) vertices \((n \geq 3)\), select all the correct statements.- [ ] The degree of each vertex in \( C_n \) is 2.- [ ] The total number of edges in \( K_n \) is \( C(n, 2) \).- [ ] The degree of each vertex in \( K_n \) is \( (n-1) \).- [ ] The total number of edges in \( C_n \) is \( n \).

The correct answer along with the explanation.All the given statements are correct.The degree of each vertex of the cycle graph is 2.The total number of edges in the complete graph is C(n,2).The degree of each vertex in complete graph is n-1.The total number of edges of the cycle graph is nA cycle graph contains a single cycle, which is a closed loop of vertices and edges. Each vertex in the cycle graph is connected to exactly two other vertices, one on each side of itself in the cycle. Therefore, the degree of each vertex in a cycle graph is always 2.C(n,2) means the number of ways to choose 2 vertices from n vertices. In a complete graph, each vertex is connected to every other vertex with an edge, resulting in the fully connected graph. So, to find the total number of edges in a complete graph, we can calculate the number of ways to choose 2 vertices from n vertices.A complete graph is the undirected graph in which each vertex is connected to every other vertex with an edge. Since there are n vertices in the complete graph, each vertex is connected to (n - 1) other vertices, as it should not be connected to itself. So, the degree of each vertex in the complete graph is n-1.For a cycle graph with n vertices, each vertex is connected to exactly two other vertices. As a result, each vertex contributes one edge to the cycle. Since there are n vertices in the cycle graph, there are n edges in total.Thus explanation for all correct statements is given above.