only if there exists unique path between every pair of vertices there are number of variants on the basic idea of tree rooted tree is one where designated vertex is called the rootwhich leads to parent-child relationship on the nodes an ordered tree is rooted tree in which each vertex has an ordering on its children binary treeswhich are the subject of differ from ordered trees since node may have only one child in binary treebut that node may be left or right childwhereas in an ordered tree no analogous notion exists for node with single child specificallyin binary treethere is position as well as order associated with the children of nodes as an examplethe graph in figure is tree note that its edge set is subset of the edge set of the undirected graph in figure on the facing page given graph (ve)if the graph (ve where eis treethen is referred to as spanning tree of figure tree graphs boot camp graphs are ideal for modeling and analyzing relationships between pairs of objects for examplesuppose you were given list of the outcomes of matches between pairs of teamswith each outcome being win or loss natural question is as followsgiven teams and bis there sequence of teams starting with and ending with such that each team in the sequence has beaten the next team in the sequencea slick way of solving this problem is to model the problem using graph teams are verticesand an edge from one team to another indicates that the team corresponding to the source vertex has beaten the team corresponding to the destination vertex now we can apply graph reachability to perform the check both dfs and bfs are reasonable approaches--the program below uses dfs matchresult collections namedtuple ('matchresult '('winning_team ''losing_team ')def can_team_a_beat_team_b (matches team_a team_b )def build_graph ()graph collections defaultdict (setfor match in matches graph match winning_team addmatch losing_team return graph def is_reachable_dfs (graph curr dest visited =set ())if curr =destreturn true elif curr in visited or curr not in graph return false visited add(curr