For the following simple graphs G1​=(V1​,E1​) and G2​=(V2​,E2​) (described by their vertex and edge sets) decide whether they are isomorphic. If they are then prove it, and if they are not give a convincing argument that explains why not. V1​={a,b,c,d,e}, E1​={ab,ad,ce,cd,cb,bd,be}, V2​={1,2,3,4,5}, E2​={12,14,15,24,34,35,45}

please answer both of the questions.   7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3
, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done..   8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree.    Please give proper explanation and typed answer only.

determine whether the given pair of graphs is isomorphic. Exhibit an isomorphism or provide a rigorous argument that none exists. Make sure to show what u1 maps to what v, what u2 maps to what v, etc.

Prove that the two graphs below are isomorphic.