How do I find the maximum flow from s to t of figure 2 & it’s capacity?
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A: the answer is given below:-
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- Create an SP client that analyses the edge-weighted digraph's edges in relation to a specified pair of vertices, s and t: Create a V-by-V boolean matrix where each item in row v and column w is true if and only if v->w is an edge in the edge-weighted digraphs whose weight can be raised without increasing the length of the shortest path from v to w, and false otherwise.(As you test your function, you should make sure that if your graph g is> g <- make.network('SW', 40, 2, 0.0)then every call disconnect.network(g) returns a value of 2. If you define> g <- make.network('SW', 40, 4, 0.0) Using igraph in R, write a function named disconnect.network that accepts as input a networkand takes that network and (in a while-loop) removes random edges, one at a time, until thenetwork becomes disconnected. The function should return the number of edges that had tobe removed in order to change the value of components(g)$no to a number greater than one.R-13.6 - Suppose we represent a graph G having n vertices and m edges with the edge list structure. Why, in this case, does the insertVertex function run in O(1) time while the eraseVertex function runs in O(m) time?
- Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: look at the picture sent Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above. Which statement of the following is correct? group of answer choices a) The sequence of vertices visited using a DFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. b) The sequence of vertices visited using a BFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. c) Both sequences are wrong. d) Both sequences are correct.Consider the (directed) network in the attached document We could represent this network with the following Prolog statements: link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Now, given this network, we say that there is a "connection" from a node "X" to a node "y" if we can get from "X" to "Y" via a series of links, for example, in this network, there is a connection from "a" to "d", and a connection from "c" to "f", etc.During the execution of DFS, give the conditions under which there is an edge from a vertex u with color c1 has an edge to a vertex v with color c2. Consider the following color combinations, (c1, c2)= (w,w), (w,g), (g, b) and (b,g).
- a. Build an adjacency matrix ? for this map. b. How many paths of length 2 from V5 to V1 exist? c. How many paths of length 3 from V5 to V1 exist?link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Using The above Formulate the appropriate Prolog predicate "path(X,Y,N)" which is true if (and only if) there is a path of length "N" from node "X" to node "Y". For example, there is a path of length 2 from "a" to "d": "a->b->d", but also "a->c->d", and so "path(a,d,2)" gives "true" (two times). There is also a path of length 3 from "a" to "d": "a->b->c->d". Test this predicate out on the above network to verify whether or not it is working correctly. Once this is working correctly, note now, that e.g., "path(a,e,N)." will give multiple answers:Which of the following is not TRUE for a K - map ? o overlapping of groups is not allowed O No of members in a group is 1,2,4,8 or 16 in a 4 variable K Map o Grouping of 1's gives a SOP expression O All given options are TRUE o When grouping , larger groups are advisable
- Consider the following flow network. The figure describes a flow ? and the capacity of the edges: if (?, ?) appears next to an edge ?, then the capacity of the edge ?ₑ is ?, and the flow ?ₑ that goes through ? in ? is ?. For example, if ? = (?, ?₁), then ?ₑ = 2 and ?ₑ = 1. 1. Draw the residual network ? & of the above flow ?. [Draw a graph containing all the nodes, edges, and the values on the edges]. 2. Find an augmenting path that will increase the flow by 1. You only need to list the vertices in the path and indicate the resulting flow in the following figure (using the same notation as the above figure). 3. Find a minimum ?-? cut in the graph (where the weight of an edge is its capacity). Briefly justify why the cut you found is a minimum cut.Sensitivity. Create an SP client that runs a sensitivity analysis on the edges of an edge-weighted digraph in relation to a given pair of vertices s and t: Create a V-by-V boolean matrix so that, for each v and w, the entry in row v and column w is true if v->w is an edge in the edge-weighted digraphs whose weight can be raised without increasing the shortest-path length from v to w, and false otherwise.Find the number of paths between c and d in the following graph of length 2. There are blank paths of length 2.