of design an efficient algorithm thatgiven an -node free tree tcomputes center of is the center uniqueif nothow many distinct centers can free tree havec- show thatif is bfs tree produced for connected graph gthenfor each vertex at level ithe path of between and has edgesand any other path of between and has at least edges - the time delay of long-distance call can be determined by multiplying small fixed constant by the number of communication links on the telephone network between the caller and callee suppose the telephone network of company named rt& is free tree the engineers of rt& want to compute the maximum possible time delay that may be experienced in long-distance call given free tree tthe diameter of is the length of longest path between two nodes of give an efficient algorithm for computing the diameter of - company named rt& has network of switching stations connected by high-speed communication links each customer' phone is directly connected to one station in his or her area the engineers of rt& have developed prototype video-phone system that allows two customers to see each other during phone call in order to have acceptable image qualityhoweverthe number of links used to transmit video signals between the two parties cannot exceed suppose that rt& ' network is represented by graph design an efficient algorithm that computesfor each stationthe set of stations it can reach using no more than links - explain why there are no forward nontree edges with respect to bfs tree constructed for directed graph -