Refer to the following network flow and state the min cut, of the graph G. --2/2- 3/7 6/6 -5/5 1/1 O (s,v1),(s,v3),(s,v2) O (v4,t).(v3,t).(v5,t) O (s,v2).(v2,v3),(v2,v5) 0/3 (v1,v4), (v1,v3),(s,v3),(s,v2) -6/9 4/5 -2/3 V₂ 6/6 6/8
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- Incorrect Question 1 Refer to the following network flow and state the min cut, of the graph G. -2/2 3/7 6/6 -5/5 (s.v1),(s,v3).(s.v2) 1/1 O (v1,v4), (v1,v3),(s,v3),(s,v2) (v4,t).(v3,t).(v5,t) 0/3 (s,v2).(v2,v3),(v2,v5) -6/9 4/5 -2/3 6/6 6/84. (1) Draw a transition graph for the dfa M={Q,E,8,q,,F ), where Q={q,,91»92 }; E = {a,b},F = {qo,92} and ở is definded as S(90,a) = q,,8(q,b) =q,,5(q,,a)=q0,8(q,,b) =q2,8(q2,a) =q2,8(q2,b) =q2 (2) Give the language accepted by the above dfa.0/16 0/12 0/8 0/4 22 0/8 0/5 0/11 VA 0/13 0/14 V5 0/2 0/11 0/10 Each edge is annotated with the current flow (initially zero) and the edge's capacity. In general, a flow of x along an edge with capacity y is shown as x/y. (a) Show the residual graph that will be created from this network with the given (empty) flow. In drawing a residual graph, to show a forward edge with capacity x and a backward edge with capacity y, annotate the original edge *; y. (b) What is the bottleneck edge of the path (S, V₁, V3, V5, t) in the residual graph you have given in answer to part (a) ? (c) Show the network with the flow (s, V₁, V3, V5, t) that results from augmenting the flow based on the path of the residual graph you have given in answer to part (a). (d) Show the residual graph for the network flow given in answer to part (c). (e) What is the bottleneck edge of the path (s, v3, v4, t) in the residual graph you have given in answer to part (d) ?
- What is the number of connected components for each of the following graphs? (a) (b) (c) (d) 3 4 2 a. U. Z X a. X b. V₁ • b V y 2₂ V4 C ● V3 W ● X Ⓡ g h →Plot the functions x, x2, exp(-x), exp(-x2) on a single graph for x between 0 and 5. Repeat the previous question where you plot the function on four different graphs (two rows and two columns). Please use phyton3 to answer thisplot these function in single graph f(x1) : 3x^3-26x+10 with - symbol with blue color f(x2) : 9x^2-26 with - symbol with red color f(x3) = 18x with . symbol with black color x = -2 to 4 with increment of 0.01
- Use A algorithm to find the solution path for the following graph where the h(n) for the states are {(S, 2), (A, 3), (B, 5), (C, 4), (D, 20), (E, 9), (F, 7), (H, 8), (G, 0)}. A 3 -5 F 6. 1. E H(1) Given a weighted directed graph G = (V, E, w), where V = {1, 2, 3, 4}, E ={(1,3), (2,1), (2,4), (3,2), (4,1), (4,3)}, and w(1,3) = −2, w(2,1) = 1, w(2,4) = 2,w(3,2) = 4, w(4,1) = −3, w(4,3) = 3. (a) Represent the graph G graphically;(b) Run SLOW-ALL-PAIRS-SHORTEST-PATHS on the above graph and show the matricesL(k) that result for each iteration of the loop. (2) Discuss how to use the Floyd-Warshall algorithm to detect a negative-weight cycle. (3) The essence of Johnson’s algorithm is re-weighting so that a transformed graph has no negativeweight edges, which enables the use of Dijkstra’s algorithm. Let us modify Johnson’s algorithmsuch that G' = G and s be any vertex. (a) Give a counter example (i.e. a simple weighted and directed graph) to show thismodification is incorrect assuming ∞ − ∞ is undefined(b) Show (using logical arguments) this modification produces the correct results when a givenG is strongly connected.Calculate the biggest graph with E = 10V that your computer and programming system could manage to within a factor of 10 if you were to apply Dijkstra's technique to find all of its shortest paths in within 10 seconds.
- -With respect to the performance model, it should be implemented efficiently. Your answer Ring the network in a ring topology comes back around to the first node, creating a complete circuit. to a bus network, rings have nodes daisy chained, but the end of Your answer ----This part includes defining the problem, designing the corresponding model, and devising a set of experiments for the formulated simulation model.Construct an undirected network diagram using the given set of nodes and arcs, also find the shortest path and distance from node A to node E using Dijkstra’s algorithm. Nodes {A, B, C, D, E} Arcs {(AB)=1, (BC)=2, (AC)=7, (BD)=3, (DC)=2, (DE)=6, (CE)=1}Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions for z = 3x2 + y2 + 3xy – 7x – 8y + 10. Please solve this problem mathematically and draw a 2D graph to show the covered domain for x and y. Please use MATLAB