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- NO.: DATE: problemr. ldentify are adjarent- the pouowing Ure graph theory to volve the and detemine when the two rer ticer rertex There ae coupler a porty. Vuppore each one at will vhake handr with every other perron Once, except handr mortN couple they nill other tach not rhake For rach How many uhake handr are There? with Make a graph preventation.Q3. Find the DFS and BFS for the following directed graph.(Start from 0) 2 3 4 5 6 8 04 Fznloin Mastor Thoorom Uging Mostor Thoorom solvod the followiH.w: show that Let x be a e dge of Connected graph G. The following statements are equivalent. (1) X is X is a bridge of G (2) X is not on any eycle of G ® There exist vertices u and vof G such the ecdgex is on every path goning u and V O There exists a pardition of V into su bsets ų and w such that for any verticesUEU and w the edge x ison every path joining u and w
- Dhow that the followings are bipartites graph by dividing their vertices into 2 subsets A and B, such that every edge connects a vertex in A to a vertex in B. a f C C d. e J to moide bid D el usd C F B.Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.Solve the above problem using adjacency list representation.In the attached graph each vertex B-J is a person who has not been exposed to virus. The red verteces are persons who have been vaccinated. Vertex has the virus. Due to the mutation rate it will take 35exposures to infect a vaccinated person, but only one to infect and unvaccinated person. Write a program which Starts at A and infects everyone.what is the most efficient way to infect everyone.
- I A E H F В G Suppose you run a topological sort on the shown graph starting at vertex B. Use the rule that when DFS has a choice of nodes to visit, it visits them in alphabetical order. What's the first vertex in the resulting topological order? What is the second? What is the third? What is the fourth?Find a large weighted graph on the web—perhaps a mapwith distances, telephone connections with costs, or an airline rate schedule. Write aprogram RandomRealGraph that builds a graph by choosing V vertices at random andE edges at random from the subgraph induced by those verticeGiven the following Graphs: Graph A: В 12c 1 4. E F G- H 4 J K 3 Graph B: Graph B is the undirected version of Graph A. 3.
- Let 6 be a simple comected yaph wich vertiles Where n isan number greuker than 2. which one Of the following statements is Of Aruc's theuems Por the Con tapositive graphs A) tea st cnt) Hamil tonian cyue EF ewy rky of G is adsacent to ut 12 vertiles I thn 6 hus B) If 6 hus no lami toniun lycue ten every verter of G j adjacent to at most CntD/2 vertices C) IP G hos no fuleriun Gue then ealh Lertex of 6 is ad jHlent je SS than Cntil2z ertices to D:) Eury urtex Of C has deyrelt at mast nl22 * 6 hus no Hamilronian (41'eWrite a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (6 Marks)(i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.Given a graph that is a tree (connected and acyclic). (I) Pick any vertex v.(II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance.(III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are truea. p is the longest path in the graphb. p is the shortest path in the graphc. p can be calculated in time linear in the number of edges/vertices