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partitioned into two disjoint subsets X and Y so that every edge connects a vert

ID: 3567993 • Letter: P

Question

partitioned into two disjoint subsets X and Y so that every edge connects a vertex in X with a vertex in Y . (One can also say that a graph is bipartite if its vertices can be colored in two colors so that every edge has its vertices colored in different colors; such-graphs are also called 2-colorable.) For example, graph (i) is bipartite while graph (ii) is not. a. Design a DES-based algorithm for checking whether a graph is bipartite. b. Design a BFS-based algorithm for checking whether a graph is bipartite. Q3. Show how depth-first search and breadth-first search work on the graph in the fi that the DFS procedure considers the vertices in alphabetical order, and assume is ordered alphabetically. State the node traversal order for each search method.

Explanation / Answer

In case of DFS: q, s, v, w, t, x, z, y, r, u

In case of BFS: q, s, t, w, v, x, y, z, r, u

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. One starts at theroot (selecting some arbitrary node as the root in the case of a graph) and explores as far as possible along each branch before backtracking.

In a BFS (breadth first search), you start at the root node, and then scan each node in the first level. Then you continue scanning the second level and the third level, and so on until you