Trace Floyd's algorithm for the all-pairs shortest path problem defined over a digraph with vertices V= {1, 2, 3, 4) and whose cost matrix is given below: [0 11 0 0482 ∞ 1 2805 201 630

give an example of a graph on n vertices where ford and fulkerson algorithm achieve its worst time complexity

Q23. * The following Adjacency Matrix represents 1 2 3 4 5 6 1010000 2 1 0 1 1 0 0 3 0 1 0 0 1 0 4 0 1 0 0 1 0 5 0 0 1 1 0 1 0 0 0 1 0 6 0 Undirected Unweighted Graph Undirected Weighted Graph O Directed Unweighted Graph O Directed Weighted Graph

Discrete mathematics. Let G = (V, E) be a simple graph4 with n = |V| vertices, and let A be its adjacency matrix of dimension n × n. We want to count the L-cycles : such a cycle, denoted by C = u0u1 · · · uL with  uL = u0 contains L distinct vertices u0, . . . , uL-1 et L edges E(C) = {uiui+1 | 0 ≤ i ≤ L − 1} ⊆ E. Two cycles are distinct if the edge sets are different : C = C' if and only if E(C) = E(C'). We define the matrices D, T, Q, the powers of A by matrix multiplication : D = A · A = A2,   T = A · D = A3,   Q = A · T = A4. Consider the values on the diagonals. Prove that the number of 3-cycles N3 in the whole graph is N3 = 1/6 ∑ u∈V   Tu,u

Please help with algorithm no coding needed

3. Given the graph below. Illustrate Dijkstra algorithm to find the shortest path from vertex s as the source. G 10 15 2 2 5 d

Explain the Bellman-Ford Algorithm using the Single Source Shortest Path Algorithm (given a graph with a negative cycle).

Design an O(E) time algorithm for recognizing a palmpolygon P where E is the number of visible pairs of vertices in P