A connected simple graph G has 16 vertices and 117 edges. Prove
G is Hamiltonian and prove G is not Eulerian


A connected simple graph G has 16 vertices and 117 edges. Prove G is Hamiltonian and prove G is not Eulerian
true or false
Can a simple connected graph of n vertices and n-1 edges admit a chain or an Eulerian turn.
49.12. Let G be a graph with n 2 2 vertices. a. Prove that if G has at least ("21) +1 edges, then G is connected. b. Show that the result in (a) is best possible; that is, for each n 2 2, prove there is a graph with ("2) edges that is not connected.
49.12. Let G be a graph with n 2 2 vertices. a. Prove that if G has at least ("21) +1 edges, then G is...
Draw a simple undirected graph G that has 12 vertices, 18 edges, and 3 connected components. Why would it be impossible to draw G with 3 connected components if G has 66 edges?
Choose the true statement. If a graph G admits an Eulerian path, then G is connected. If a graph G admits an Eulerian path, then G admits a Hamiltonian path. If a graph G admits a Hamiltonian path, then G admits an Eulerian path. the four other possible answers are false If a graph G is connected, then G admits an Eulerian path.
(a) Let L be a minimum edge-cut in a connected graph G with at least two vertices. Prove that G − L has exactly two components. (b) Let G an eulerian graph. Prove that λ(G) is even.
Let G be a simple graph with at least four vertices. a) Give an example to show that G can contain a closed Eulerian trail, but not a Hamiltonian cycle. b) Give an example to show that G can contain a closed Hamiltonian cycle, but not a Eulerian trail.
R-13.2: Let G be a simple connected graph with n vertices and m edges. Explain why O(log m) is O(log n).
A.) Prove that if some graph G is an Eulerian graph, the L(G) {the line graph of G} is also Eulerian. B.) Find a connected non-Eulerian graph for which the line graph is Eulerian.
Let G be a graph with n vertices and n edges. (a) Show that G has a cycle. (b) Use part (a) to prove that if G has n vertices, k components, and n − k + 1 edges, then G has a cycle.
Show that a connected regular graph with an odd number of vertices is always Eulerian.