1. Give an adjacency-list representation for a complete binary tree on 7 vertices. Give an equivalent adjacency - matrix representation. Assume that vertices are numbered from 1 to 7 as in a binary heap?
2. Is Minimum Spanning Tree for an Undirected connected graph unique, Justify your answer?
3. Modify the kruskal's algorithm using priority queue data structure?
b) There are two well known algorithm for finding minimum spanning trees. Point out the difference between Prim's algo and kruskal algo in term of construction in Minimum Spanning tree?
Part B
4. Analyze the following properties of BFS and DFS for an Acyclic Tree without making any assumptions.
a.) Optimality
b.) Completeness
c.) Space Complexity
d.) Time Complexity
Propose an algorithm which is a hybrid of both BFS and DFS and ensures better characteristics compared to both BFS and DFS.
5. Modify Prim's or Kruskal's algorithm to find a diameter bounded minimum spanning tree of a complete graph. A diameter bounded minimum spanning tree is a spanning tree having least cost and diameter not greater than a bound .
6. Compare and contrast among Dijkstra's Algorithm, Ford Algorithm and WFI Algorithm to find shortest path.