What makes a graph traversal

Representation of Graphs Graph data structure is represented using the following representations. Adjacency Matrix Adjacency List. Adjacency Matrix In this representation, the graph can be represented using a matrix of size n x n, where n is the number of vertices. Here, 1 represents that there is an edge from row vertex to column vertex, and 0 represents that there is no edge from row vertex to column vertex. Directed graph representation. Adjacency list In this representation, every vertex of the graph contains a list of its adjacent vertices.

If the graph is not dense, i. Adjacency List. Graph traversals Graph traversal is a technique used to search for a vertex in a graph.

It is also used to decide the order of vertices to be visited in the search process. A graph traversal finds the edges to be used in the search process without creating loops.

This means that, with graph traversal, we can visit all the vertices of the graph without getting into a looping path. Step 2: Select any vertex as the starting point for traversal. Visit that vertex and push it on to the Stack. Step 3: Visit any one of the adjacent vertices of the vertex, that is at top of the stack and is not visited, and push it on to the stack. Step 4: Repeat step 3 until there are no new vertices to visit from each vertex on top of the stack.

Step 5: When there is no new vertex to visit, use backtracking and pop one vertex from the stack. Step 6: Repeat steps 3, 4, and 5 until stack becomes Empty. One is based on the adjacency of vertices, and the other is based on incidence of vertices and edges. Same applies to all vertex.

The adjacency list data structure should immediately remind you of hash tables with chaining;the two data structures are identical. An adjacency list is an array of linked lists, one list per vertex. Each linked list stores the neighbors of the corresponding vertex. For example for a vertex there are edges leading to neighbors as b,d and e.

So its respective linked list contains vertex that are connected via edge. A weighted graph or weighted digraph is a graph or di-graph with numbers assigned to its edges. These numbers are called weights or costs.

An interest in such graphs is motivated by numerous real-world applications, such as finding the shortest path between two points in a transportation or communication network or the traveling salesman problem. Where Edges represent streets and vertices represent crossings.

Graph theory underlies the Internet. The Cosmos HackAtom is here! Get feral when you answer to the greatest interview in history Share your philosophy. An intro to Data Structures: Graphs and its traversal algorithms is an intro to non-linear data structures.

Graphs can be undirected or directed, directed, cyclic or acyclic mostly directed , or weighted. DFS of a graph uses stack, but inorrder traversal of a tree is recursive.

Question 2 Explanation:. Question 3. What are the appropriate data structures for following algorithms? Question 3 Explanation:. Question 4. The Breadth First Search algorithm has been implemented using the queue data structure.

One possible order of visiting the nodes of the following graph is. Question 4 Explanation:. In BFS all adjacent must be visited before adjacent of adjacent. Thus, R is visited before O. Question 5. Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new unvisited vertex visited after visiting u in the traversal.

Which of the following statements is always true? Question 5 Explanation:. In DFS , if 'v' is visited after 'u', then one of the following is true. Back tracking is coming back to the vertex from which we reached the current vertex. The perfect place for easy learning Place your ad here. Previous Next. Step 1 - Define a Stack of size total number of vertices in the graph.